machine_learning_basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression for converting binary to decimal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0]\n",
      " [0 0 1]\n",
      " [0 1 0]\n",
      " [0 1 1]\n",
      " [1 0 0]\n",
      " [1 0 1]\n",
      " [1 1 0]\n",
      " [1 1 1]]\n",
      "[0, 1, 2, 3, 4, 5, 6, 7]\n"
     ]
    }
   ],
   "source": [
    "X = np.matrix([[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]])\n",
    "y = [0,1,2,3,4,5,6,7]\n",
    "print X\n",
    "print y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8, 3)\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "print X.shape\n",
    "print len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0]] ---> 0\n",
      "[[0 0 1]] ---> 1\n",
      "[[0 1 0]] ---> 2\n",
      "[[0 1 1]] ---> 3\n",
      "[[1 0 0]] ---> 4\n",
      "[[1 0 1]] ---> 5\n",
      "[[1 1 0]] ---> 6\n",
      "[[1 1 1]] ---> 7\n"
     ]
    }
   ],
   "source": [
    "for count, instance  in enumerate(X):\n",
    "    print instance, '--->', count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "regr = linear_model.LinearRegression()\n",
    "# Train the model using the training sets\n",
    "regr.fit(X, y)\n",
    "# Make predictions using the testing set\n",
    "y_pred = regr.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  4.44089210e-16,   1.00000000e+00,   2.00000000e+00,\n",
       "         3.00000000e+00,   4.00000000e+00,   5.00000000e+00,\n",
       "         6.00000000e+00,   7.00000000e+00])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.,  2.,  1.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regr.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Logistic regression for classifying the binary values above 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0]\n",
      " [0 0 1]\n",
      " [0 1 0]\n",
      " [0 1 1]\n",
      " [1 0 0]\n",
      " [1 0 1]\n",
      " [1 1 0]\n",
      " [1 1 1]]\n",
      "[0, 0, 0, 0, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "X = np.matrix([[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]])\n",
    "y = [0,0,0,0,1,1,1,1]\n",
    "print X\n",
    "print y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8, 3)\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "print X.shape\n",
    "print len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0]] ---> 0 ---> 0\n",
      "[[0 0 1]] ---> 1 ---> 0\n",
      "[[0 1 0]] ---> 2 ---> 0\n",
      "[[0 1 1]] ---> 3 ---> 0\n",
      "[[1 0 0]] ---> 4 ---> 1\n",
      "[[1 0 1]] ---> 5 ---> 1\n",
      "[[1 1 0]] ---> 6 ---> 1\n",
      "[[1 1 1]] ---> 7 ---> 1\n"
     ]
    }
   ],
   "source": [
    "for count, instance, label in zip(range(len(y)),X,y):\n",
    "    print instance, '--->', count, '--->', label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "logistic = linear_model.LogisticRegression()\n",
    "# Train the model using the training sets\n",
    "logistic.fit(X, y)\n",
    "# Make predictions using the testing set\n",
    "y_pred = logistic.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "print y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.24054754, -0.11269202, -0.11269202]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logistic.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.77565930715079745"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / (1 + np.exp(-1.24054754))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47185677242092089"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / (1 + np.exp(0.11269202))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression for profit prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# lets solve the real problems\n",
    "# implementing linear regression with one variable to predict profits for a food truck."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Population   Profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/linear_Reg_1.txt', header=None, names=['Population', 'Profit'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fedd88a7f10>"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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a69dvv8ztE6gBABiFXe+hTvKzw79/fGclAQDA/rZZoP6xJF+T5F/UWl87gnoAAGCibBao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\nAAA08P8D7GkyjL0+/oEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedd8d86c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create a function to compute the cost of a given solution\n",
    "# y = X * W^T\n",
    "# ((X * w^T)- y)^2 = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def computeCost(X, y, W):\n",
    "    inner = np.power(((X * W.T) - y), 2)\n",
    "    return np.sum(inner) / (2 * len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.insert(0, 'Ones', 1)\n",
    "cols = data.shape[1]\n",
    "X = data.iloc[:,0:cols-1]\n",
    "y = data.iloc[:,cols-1:cols]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# see what is there in X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ones</th>\n",
       "      <th>Population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Population\n",
       "0     1      6.1101\n",
       "1     1      5.5277\n",
       "2     1      8.5186\n",
       "3     1      7.0032\n",
       "4     1      5.8598"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# see what is there in y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Profit\n",
       "0  17.5920\n",
       "1   9.1302\n",
       "2  13.6620\n",
       "3  11.8540\n",
       "4   6.8233"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.matrix(X.values)\n",
    "y = np.matrix(y.values)\n",
    "W = np.matrix(np.array([0,0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# see what is there in W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0, 0]])"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((97, 2), (1, 2), (97, 1))"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, W.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.072733877455676"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computeCost(X, y, W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# finding the best values for W which satisfies ((X * w^T)- y)^2 = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradientDescent(X, y, W, alpha, iters):\n",
    "    temp = np.matrix(np.zeros(W.shape))\n",
    "    parameters = int(W.ravel().shape[1])\n",
    "    cost = np.zeros(iters)\n",
    "    for i in range(iters):\n",
    "        error = (X * W.T) - y\n",
    "        for j in range(parameters):\n",
    "            term = np.multiply(error, X[:,j])\n",
    "            temp[0,j] = W[0,j] - ((alpha / len(X)) * np.sum(term))\n",
    "            \n",
    "        W = temp\n",
    "        cost[i] = computeCost(X, y, W)  \n",
    "    return W, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "iters = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.24140214  1.1272942 ]]\n"
     ]
    }
   ],
   "source": [
    "final_W, cost = gradientDescent(X, y, W, alpha, iters)\n",
    "print final_W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.5159555030789118"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computeCost(X, y, final_W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# lets visualize what we have learnt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fedd8c1f510>"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sFb7ZZjB1Kvzv/8Kaa7bdOdVqTKglSZLqyeuKiXPnJsuD9+sHdXVJqccVV0CP\nHq1/LrUZa6glSZJWok27fCxcCLffntRH7757kkT37du651CzNKeG2oRakiQpX2KEBx6ACy+EzTeH\na66BnXZKOyrV49LjkiRJheqpp+D88+Grr+DXv4bBg9OOSK3EhFqSJKktvfJKkkhPnQpXXglHHQVd\nnMbWkfhuSpIktYV33kn6R++7Lxx4IEyaBEcfbTLdAfmOSpIktaYZM+CMM2DgQNhqK5gyBX78Y+je\nPe3I1EbyklCHEDYLITwVQngjhPBaCOGM3Pb1Qwh/DSG8FUJ4IoRgjxhJktQ+zZkDl14K22wDISQj\n0pdcAuuum3ZkamP5GqH+CvjfGOO2wC7Aj0MI/YDzgSdjjFsDTwEj8xSPJElS61iwAH71q2Q0eupU\nePFF+OUvYcMN045MeZKXSYkxxo+Bj3PffxFCmARsBhwM7JV72B3AeJIkW5IkqbAtXgz33gujRiXJ\n9OOPw7e+lXZUSkHeu3yEEMqAbwEvABvFGKdDknSHELyVkyRJhS1G+OtfYeRIKCqC226D8vK0o1KK\n8ppQhxDWAR4AzsyNVC+/WkuDq7eMHj166feDBg1i0KBBbRGiJElSw6qrkxZ477+fLBl+2GFJvbTa\nrfHjxzN+/PgWHSNvKyWGELoBjwCPxxh/mds2CRgUY5weQtgYGBdj3GYlz3WlREmSlJ6pU5PVDZ97\nLplo+MMfQjeX8+iImrNSYj7b5t0OvLkkmc55CDgh9/3xwJ/zGI8kSdKqffQRDB8Ou+4KO+yQJNan\nnGIyrWXkq23ebsAxwN4hhJdDCBNCCN8HrgUGhxDeAr4DXJOPeCRJklZp1qxkRPqb30za3r31VlIz\nvdZaaUemApSvLh/PAV0b2P3dfMQgSZK0Wl9+Cb/+NVx7LRxwALz8Mmy+edpRqcD5eYUkSdKiRXD3\n3XDxxUnru3HjYNtt045K7YQJtSRJ6rxihEcfTco5evSAe+6B3XZLOyq1MybUkiSpc/rnP+G882Dm\nTLj6ajjwQFvgqVny2eVDkiQpfW++CYccAkcfDRUVMHEiHHSQybSazYRakiR1DtOmJQn0oEGwxx4w\nZQqccAJ0bahvgtQ4JtSSJKljmzkTzj03mWy40UZJIv2Tn8Caa6YdmToIE2pJktQxzZuXtL/beuuk\nr/RrryXLha+3XtqRqYNxUqIkSepYvvoKfvtbuPRS2HlnePbZJKmW2ogJtSRJ6hhihD/+ES64ADbZ\nBP7wB/gs2DojAAAgAElEQVT2t9OOSp2ACbUkSWr/nn4azj8f6urgF7+Affaxa4fyxoRakiS1X6++\nmizKMnkyXH45DB0KXZwipvzyN06SJLU/774LP/hBMhK9775JQn3MMSbTSoW/dZIkqf3IZuGss2Cn\nnWCLLWDqVDj9dOjePe3I1ImZUEuSpML3xRdJScc228CiRclqh5deCuuum3Zkkgm1JEkqYAsXwpgx\nsNVWMGkS/Otf8KtfJQu0SAXCSYmSJKnwLF4M998PF14IW24Jjz4KO+yQdlTSSplQS5KkwvLkk0kL\nvBDgN7+BvfdOOyJplUyoJUlSYXjppSSRrqmBK6+EI4+0l7TaBWuoJUlSuqZOhSFD4MAD4fDDkwmH\nRx3VKZLpbDZLdXU12Ww27VDUAibUkiQpHR9/DCNGwC67QP/+SWI9fDgUFaUdWV5UVY0lk+nH4MHD\nyWT6UVU1Nu2Q1Ewhxph2DKsVQojtIU5JktQIs2fDz36WdO84/ni44ALYYIO0o8qrbDZLJtOPurpx\nQH9gIsXF5dTWTqa0tDTt8Dq1EAIxxiZ9POIItSRJyo/58+GXv4S+feG992DCBLj++k6XTAPU1NTQ\nvXsZSTIN0J+iogw1NTXpBaVmM6GWJElta9EiuOsu6Ncv6eDx5JNwxx2QyaQdWWrKyspYsKAGmJjb\nMpGFC2spKytLLyg1m10+pCbIZrPU1NRQVlbmR3KStDoxwuOPJ5071lkH7rwT9tgj7agKQmlpKZWV\nY6ioKKeoKMPChbVUVo7x35Z2yhpqqZGqqsZSUTGC7t2TUYXKyjEMHTok7bAkqTC98AKcdx5ks3D1\n1XDQQZ2ia0dTOVBTeJpTQ21CLTWCk0ckqZEmT04mGVZXw+jRyaTDbn4grvbDSYlSG3HyiCStxgcf\nwCmnJCUdu+wCU6ZARYXJtDoFE2qpEZw8IkkN+OyzpEa6f39Yf/0kkf6//4Pi4rQjk/LGhFpqhCWT\nR4qLyykpGUBxcbmTRyR1bnV18NOfwlZbwaefwquvwrXXJkm11MlYQy01gZNHJHV6X32VtLwbPRoG\nDoQrr4Rttkk7KqnVOClRkiS1jRjhz39OJhyWliaj0Tvv3GqHd8BChcJJiZIkqfX94x+w225w8cVw\n3XUwfnyrJtNVVWPJZPoxePBwMpl+VFWNbbVjS/ngCLUkSVq511+HkSPhtdfgssvgmGOga9dWPYVt\nSVVoHKGWJEktV1sLJ5wA3/lO8vXWW3Dcca2eTINtSdUxmFBLkqTEp5/CT34CAwZAnz5JC7yzzoI1\n1mizU9qWVB2BCbUkSZ3d3LlJt46tt07a4b3xBlx+OfTo0eanti2pOgJrqCVJ6qwWLoTKyqQ+es89\n4YorYMstUwnFLh8qFLbNkyRJqxcjPPAAXHghZDJw9dWw005pRyUVhOYk1N3aKhhJklSAnnoqWSp8\n0SL49a9h8OC0I5LaPRNqSZI6g5dfThLpt99O6qWPPBK6OJVKag3+nyRJUkf29tswbBjstx8cfDC8\n+SYMGWIyLbUi/2+SJKkjmj4dTj8dvv1t2GYbmDoVRoyA7t3TjkzqcEyoJUnqSObMgUsugW98IxmF\nnjQJRo2CddZJOzKpwzKhliSpI5g/H268Efr2hXfegRdfhF/+EmxBJ7U5JyVKktSeLV4M994LF10E\n/frBE0/A9tunHZXUqZhQS5LUHsWYJM8jRyZ10bffDoMGpR2V1CmZUEuS1N5UV8N558GHH8JVV8Gh\nh0Jo0joUklqRNdSSJLUXU6Yk/aMPPRSGDoXXX4fDDjOZllJmQi1JUqH78EM49VTYbbdkifApU+Dk\nk6GbHzRLhcCEWpKUumw2S3V1NdlsNu1QCsvnn8MFF8B220GPHvDWW0mpx1prpR2ZpHpMqCVJqaqq\nGksm04/Bg4eTyfSjqmps2iGl78sv4ec/h622go8/hldegZ/+FHr2TDsySSsRYoxpx7BaIYTYHuKU\nJDVNNpslk+lHXd04oD8wkeLicmprJ1PaGfsnL1oEd92VLMyyww5w5ZWw7bZpRyV1KiEEYoxNmphg\n8ZUkKTU1NTV0715GXV3/3Jb+FBVlqKmp6VwJdYzw8MNJecf668M99yT10pLaBRNqSVJqysrKWLCg\nBpjIkhHqhQtrKSsrSzWuvHruuaQu+vPP4eqr4YAD7NohtTPWUEuSUlNaWkpl5RiKi8spKRlAcXE5\nlZVjOsfo9BtvwMEHw7BhSceOV1+FAw80mZbaobzUUIcQKoEDgOkxxv65bZcAJwMzcg+7IMb4lwae\nbw21JHVg2WyWmpoaysrKOn4y/d57SY30o4/C+efDiBGw5pppRyUppzk11PlKqHcHvgDuXC6hnhNj\nvL4RzzehliS1bzNnJiUdlZXwox/BuecmrfAkFZTmJNR5KfmIMT4LfLaSXX6uJUnq2ObNg2uuSVrg\nzZ6drG545ZUm01IHknYN9WkhhFdCCLeFEPzLIknqOL76Cm69NUmkX3opmXx4yy3Qu3fakUlqZWl2\n+RgDXBZjjCGEK4DrgYqGHjx69Oil3w8aNIhBgwa1dXySJDVdjPDHPyYt8Hr3hgcfhP/5n7SjktSA\n8ePHM378+BYdI28Lu4QQMsDDS2qoG7svt98aaklKQaeaLNgaxo9PJhrOn5+UeXzve3btkNqZgq2h\nzgnUq5kOIWxcb99hwOt5jEWStBouCd4Er74K++4LP/whnHFGUuKxzz4m01Inka8uH/cAg4BewHTg\nEqAc+BawGKgBTo0xTm/g+Y5QS1IeuSR4I737LowaBU8+CRdeCKeeCt27px2VpBYo2KXHY4zDVrL5\nt/k4tySp6VwSfDWyWbjiCrj7bjj9dLj5Zlh33bSjkpSStLt8SJIK0LJLgkOnXBJ8Zb74Ai67DLbZ\nJpl8OGkSjB5tMi11cibUkqQVdOolwVdmwQK46Sbo2xfeegv+/W+48UbYcMO0I5NUAPLW5aMlrKGW\npHR0+i4fixfDffcl9dF9+yYrHe6wQ9pRSWpDBbv0eEuZUEuS8u5vf4PzzoNu3ZIWeHvvnXZEkvKg\nYCclSpLUbrz4YtJLetq0ZInwww+3/Z2kVbKGWpIkgKlTYcgQOPhgOPJIeP11OOIIk2lJq2VCLUnq\n3D7+GEaMgF12gW99K0msTz0ViorSjkxSO2FCLUnqnGbPThZl2XZbKC5OuneMHAlrrZV2ZJLaGRNq\nSVLnMn8+/OIXSdeOadNgwgT4+c+hV6+0I5PUTjkpUVKjdfoWamrfFi2C3/8eLr4YttsuWS58u+3S\njkpSB+AItaRGqaoaSybTj8GDh5PJ9KOqamzaIUmNEyM8+mhSH/3//h/cdRc8/LDJtKRWYx9qSauV\nzWbJZPpRVzcO6A9MpLi4nNrayY5Ut2Od4hOHF15Iekl/8glcdRUcdJBdOyStUnP6UDtCLWm1ampq\n6N69jCSZBuhPUVGGmpqa9IJSi3T4TxwmTYLDDkva351wAkycmLTDM5mW1AZMqCWtVllZGQsW1AAT\nc1smsnBhLWVlZekFpWbLZrNUVIygrm4cs2a9RF3dOCoqRpDNZtMOreXefx9OOgn22itpgzdlCpx4\nInTtmnZkkjowE2pJq1VaWkpl5RiKi8spKRlAcXE5lZVjOm6ZQAfXIT9x+OyzpLRj++2htDRJpP/v\n/5J2eJLUxqyhltRonaLmthPoUDXxdXXwq1/Bz34GhxwCo0fDppumHZWkdqzNaqhDCLs1Zpukjq20\ntJSBAwe2v6RLy+gQnzh89RXcdhtstRX861/wj3/ArbeaTEtKRaNGqEMIE2KMA1a3ra04Qi1Jra9d\nfuIQI/zpT3DBBbDRRnDttfDtb6cdlaQOpDkj1Ktc2CWEsAuwK1AaQvjfertKAGd4SFI7Vlpa2n4S\naYBnnknqpOfNg+uvh+9/364dkgrC6lZK7A6sk3vcuvW2zwaOaKugJEla6rXXYORIeOMNuPxyGDYM\nujinXlLhaGzJRybGWJuHeBo6vyUfktTZ1NYmy4T/5S9Jicfw4bDGGmlHJamDa4uSj1/EGM8Cbgoh\nrJDRxhgPamKMkiSt2pJVDe+4A378Y5g6FUpK0o5Kkhq0upKPO3P/va6tA5EkdXJz58INN8AvfgFD\nhiQlHhtvnHZUkrRaq0uofwZ8B9gvxnheHuKRJHU2CxcmLfAuvxz23BNeeAG23DLtqCSp0VaXUG8S\nQtgVOCiEcC+wTD1JjHFCm0UmSerYYoT774cLL4SvfQ0efhh23DHtqCSpyVY5KTGEcARQAewOvLjc\n7hhj3LsNY6sfh5MSJakj+fvf4fzzk6T6mmvgu99NOyJJApo3KbGxXT5GxRgvb3ZkLWRCLUkdxIQJ\nSSL9zjvJxMMjjrAFnqSC0mYJde7gBwF75n4cH2N8pInxNZsJtSS1c2+/DRddBOPHw6hRcPLJUFSU\ndlSStILmJNSNGhYIIVwNnAm8mfs6M4RwVdNDlKT/ymazVFdXk81m0w5FbWX6dDjttGR58G98I2mB\nN2KEybSkDqWxn7PtDwyOMd4eY7wd+D5wQNuFJamjq6oaSybTj8GDh5PJ9KOqamzaIak1zZkDl1yS\nJNFFRTBpUjIyvc46eTm9N2uS8qkphWvr1fu+R2sHIqn9aGmyks1mqagYQV3dOGbNeom6unFUVIww\n+ekI5s+HG2+Evn3h3XfhpZeS3tKlpXkLwZs1SfnW2IT6auDlEMLvQgh3AC8BV7ZdWJIKwcoS59ZI\nVmpqaujevQzon9vSn6KiDDU1Na0RttKweDHcfTf06wd//WvydeedUFaW1zC8WZOUhtUm1CGEADwL\n7Aw8CPwB2CXG6C2/1MoK6WPqlSXOrZWslJWVsWBBDTAxt2UiCxfWUpbn5EutIEZ4/HEYMABuugl+\n9zt45BHo33+1T20L3qxJSsNqE+pce43HYowfxRgfyn19nIfYpE6lkD6mbihxfvnll1slWSktLaWy\ncgzFxeWUlAyguLicysoxlOaxLECt4F//gr33hrPPhosvhuefh732SjUkb9YkpaGxJR8TQggD2zQS\nqRMrtI+pGxrlA1otWRk6dAi1tZN58slbqK2dzNChQ1oct/LkrbeS/tGHHw7HHAOvvw6HHQahSV2m\n2oQ3a5LSsLqlx5f4NnBsCKEGmEuyBHmMMabzmZ7UwSxJYOvqVhz5TSMRWHaUrz9LEucddtiBysox\nVFSUU1SUYeHC2hYlK6WlpSY67cmHH8Kll8KDD8I55yQ10mutlXZUKxg6dAjf/e7e1NTUUFZW5u+Y\npDbX2JUSMyvbHmOsbfWIVn5+F3ZRh5bNZslk+lFXN44lCWxxcTm1tZNTSwaqqsZSUTFimcR5yShy\nNps1WelMPv8cfvpTuOUWqKhIVjrs2TPtqCSpTbT6SokhhDWB4cCWwGtAZYzxqxZF2Qwm1OoMVpXA\npsXEuZP78stkouFPfwoHHQSjR8Nmm6UdlSS1qbZIqMcCC4F/APsCtTHGM1sUZTOYUKuzMIFVQVi0\nKCnnuOQS2HFHuPLKZIEWSeoE2iKhfi3GuF3u+27Av2OMA1oWZtOZUEtSHsQIDz8MF1yQlHRccw3s\numvaUUlSXjUnoV7dpMSFS76JMX4VCmAGtySpDTz7bFIbPWtWkkjvv39BdO2QpPZgdSPUi0i6ekDS\n2aMYmMd/u3yUtHmEOEItSW3m9deTEelXX4XLLoNjj4WuXdOOSpJS0+oj1DFG/6pKUkf03ntJjfRj\njyUj0/fdB2uumXZUktQuNXZhF0lSR/Dpp0kP6R12gE03hSlTkpUOTaYlqdlMqCWpM5g7F666Crbe\nOvn+9dfhiiugR4+0I5Okds+EWpI6soULkwVZttoKXn4Z/vlPuPlm2GSTtCOTpA6jsUuPS5LakxiT\nJcIvuCAp7fjTn2DgwLSjkqQOyYRakjqaceOSiYYLFsCNN8L3vmcLPElqQybUktRRvPIKjBwJb72V\n1EcffTR0sbJPktqaf2klqb17992kf/S++yYLskyeDMOGmUxLUp7411aS2qsZM+CMM2CnnZJJh1Om\nwGmnQffuaUcmSZ2KCbUktTdz5sCll8I22yS10ZMmwcUXw7rrph2ZJHVKJtSS1F4sWAA33fTf0ejq\navjlL2HDDdOOTJI6NSclSlKhW7wYxo6Fiy6Cvn2T5cJ32CHtqCRJOXlJqEMIlcABwPQYY//ctvWB\nsUAGqAGOijHOykc8ktQuxAh/+1vSAq+oCG67DcrLW+3w2WyWmpoaysrKKC0tbbXjSlJnk6+Sj98C\n+yy37XzgyRjj1sBTwMg8xSJJha+6Gr77XTj9dLjwQnjhhVZNpquqxpLJ9GPw4OFkMv2oqhrbaseW\npM4mxBjzc6IQMsDD9UaoJwN7xRinhxA2BsbHGPs18NyYrzglKVVTpiSlHc89B5dcAj/8IXRr3Q8T\ns9ksmUw/6urGAf2BiRQXl1NbO9mRakmdXgiBGGOTVsNKc1LihjHG6QAxxo8BZ9VI6rw++giGD4dd\nd03qo6dOhVNOafVkGqCmpobu3ctIkmmA/hQVZaipqWn1c0lSZ1BIkxJXOQQ9evTopd8PGjSIQYMG\ntXE4kpQHs2bBz34GN98MJ56YrHLYq1ebnrKsrIwFC2qAiSwZoV64sJaysrI2Pa8kFaLx48czfvz4\nFh0jzZKPScCgeiUf42KM2zTwXEs+JHUs8+fDmDFwzTWw335JX+nNN8/b6auqxlJRMYKiogwLF9ZS\nWTmGoUOH5O38klSomlPykc+Euowkod4u9/O1wMwY47UhhPOA9WOM5zfwXBNqSR3DokXw+9/DqFGw\n/fZw9dWw7baphGKXD0laUcEm1CGEe4BBQC9gOnAJ8CfgfqAPUEvSNu/zBp5vQi2pfYsx6R99/vnQ\no0cyMr377mlHJUlaTsEm1C1lQi2pXXv+eTjvPPj002RE+sADkyXDJUkFp711+ZCkjm3SJDj0UBgy\nJJlwOHEiHHSQybQkdTAm1JLU2t5/H046CfbaC3bbLencceKJ0LVr2pFJktqACbUktZaZM+Hcc5PJ\nhhtskCzScs45UFycdmSSpDZkQi1JLVVXB9deC1tvDZ9/npR2XHMNrLde2pFJkvLAhFqdSjabpbq6\nmmw2m3Yo6gi++gpuuw222gqqq+HZZ+E3v4FNN007MklSHplQq9OoqhpLJtOPwYOHk8n0o6pqbNoh\nqb2KEf74R9huu6Sn9AMPJF9bb512ZHnjzakk/Zdt89QpZLNZMpl+1NWNY8lSy8XF5dTWTnZBCzXN\n008nvaTr6pKyjn326XRdO5assti9e7KEuassSupIbJsnNaCmpobu3ctIkmmA/hQVZaipqUkvKLUv\nEyfC/vvDCSfAaafBhAnw/e93umQ6m81SUTGCurpxzJr1EnV146ioGOFItaROzYRanUJZWTKSBhNz\nWyaycGEtZWVl6QWl9qGmBo47Dr73vWQ0evJkOOYY6NI5/3x6cypJK+qc/yKo0yktLaWycgzFxeWU\nlAyguLicysoxlnuoYZ98AmefDTvuCF/7WtIC74wzYI010o4sVd6cStKKrKFWp5LNZqmpqaGsrMxk\nWiv3xRdwww3wy1/C0UfDqFGw0UZpR1VQltRQFxVlWLiw1hpqSR1Kc2qoTaglCWDhQrj1VrjiChg0\nCC6/HL7+9bSjKljenErqqEyoJampFi+G+++HCy+ELbZIOncMGJB2VJKklDQnoe7WVsFIUsF78kk4\n77ykU8ctt8B3vpN2RJKkdsiEWlLnM2FC0kv63XfhyivhiCM6bdcOSVLL+S+IpM7j7bdh6NCkn/Qh\nh8Cbb8JRR5lMS5JaxH9FJHV806cni7F8+9uw7bYwdSqMGAFFRWlHJknqAEyoJXVcs2fDxRfDN76R\nJM+TJ8NFF8E666QdmSSpAzGhltTxzJ+f9JHu2xdqa5Oa6RtugA02SDuyFWSzWaqrq126W5LaMRNq\nSR3HokVw113Qrx/87W9JF4877oBMJu3IVqqqaiyZTD8GDx5OJtOPqqqxaYckSWoG+1BLav9ihL/8\nJencsdZacO21sOeeaUe1StlslkymH3V144D+wESKi8uprZ3sQimSlCL7UEvqfP71r6SX9PTpcPXV\ncPDBSV/pegpxVb+amhq6dy+jrq5/bkt/iooy1NTUFEyMkqTGseRDUvs0eTIcfnjSQ/oHP4DXXkta\n4S2XTBdqWUVZWRkLFtQAE3NbJrJwYS1lZWXpBSVJahYTakntywcfwMknwx57JG3wpkyBigrotuIH\nbtlsloqKEdTVjWPWrJeoqxtHRcWIgpgAWFpaSmXlGIqLyykpGUBxcTmVlWMcnZakdsiEWlL78Nln\nSY10//7MW3NNJtx7L9kTT4Ti4gafsqSsIqlRhvplFYVg6NAh1NZO5sknb6G2djJDhw5JOyRJUjOY\nUEsqbHV18LOfwVZbwSef8KdLL2eDynvY+/BzV1vC0R7KKkpLSxk4cKAj05LUjtnlQ1Jh+uoruPNO\nuOQS2GknuOoqshts0OTOGFVVY6moGEFRUYaFC2uprBzjSLAkqUF2+ZDU/sUIDz0EI0dCr15w332w\nyy4A1FRXN7kzxtChQ/jud/cuuC4fkqSOw4RaWk4htlhLU16vx7PPJi3wZs9Oyjz222+Zrh3LlnAk\nI9SNKeEoLS31vZQktRlrqKV6CrXFWlrydj1efx0OOgiOPRZOPRVeeQX233+FFnh2xpAkFSJrqKUc\nV65bVl6uR21tUiP9+ONJB48f/QjWXLNRsaX1KYKfYEhSx9acGmpHqKWcQm+xlm9tej0+/RR+8hMY\nMAD69El6SZ99dqOSaUivM4afYEiSVsaEWsppDy3W8qlNrsfcuXDVVbD11jBvXlLqcfnl0KNHywNu\nY4W8SIwkKV0m1FJO/frctdfevtPX57ZqvfLChXDLLUkv6VdfZeajj1L9wx+SXcnqhoXKTzAkSQ1p\nP/+aSXkS42Jgfu6/7cPq6nqbW/fb4pZzMcIf/gAXXpiUdvz5z1RNfZuK8v3o3j0ZAc9XX+iW1j43\nt8OIJKkTiDEW/FcSptS2ZsyYEYuLe0Z4NSaZ4KuxuLhnnDFjRtqhrdI999wbi4t7xh49BsTi4p7x\nnnvubdL+NvP3v8c4cGCMO+wQ4xNPxBjze41nzJgR//3vf8cZM2a02jVYcpySkh3yey0lSXmTyzub\nlKva5UPKqa6uZvDg4cya9dLSbSUlA3jyyVsYOHBgk46Vr04Qq+vEkUrnkpdfThZl+c9/4Ior4Kij\noEtSXdaa13hVlqyO2L17GfPnv8PixZEFC56hNa6BXT4kqWOzy4fUAq01CS+fnSBWV9fb1LrfbDZL\ndXV18ybavfMODBuWLMZywAHw5ptw9NFLk2nIz8TP5ScPfvnlr1mwoJTWqn1Oq8OIJKlwmVBLOa0x\nCS/fnSBWl6A2JYFt9o3AjBlw+ukwcCD06wdTp8Jpp0H37is8NB8Ls6x4EzEY+BC7t0iS2oolH9Jy\nWvKRfr5KGupbUt5QVJRh4cLaFSb5rW4/NHMRlzlz4Oc/h1/9Klnh8MILYcMNGxVzW5ZNrOy1FBXt\nRrdu3Vd5DSRJguaVfJhQS60ordUWW9rlo0k3AgsWJC3wrrwSvvtduOwy2GKLVn9NLbGym4gWdSuR\nJHUaJtRSAWjMiHChadSNwOLFMHYsXHRR0k/66qvhW99KM+xVcvKgJKk5TKilAtEek7kGbwRihL/+\nNencUVQE114LgwalHa4kSW3ChFpSi6xwI1BdDeedBx98kIxIH3oohCb9jZEkqV0xoZYKTHscqQZg\nypRkkuE//wmjR8OJJ0I7WiZckqTmsg+1VEDy2Y+61Xz0EQwfDrvuCgMGJC3wTj7ZZFqSpFVwhFpq\nA2l1+2i2WbPgZz+Dm2+GH/4Qzj8fevVKOypJkvLOEWp1Ki1a1a+NNXWFwtR8+SVcf33StePDD+GV\nV+BnPyO7eHHBXltJkgqNCbXapUIvp8jHEtstsmgR/O53sPXW8PTT8NRTcPvt0KdPwV9bSZIKjSUf\nanfaSzlFQfajjhEeeSRpgbfeekkLvN12W7q7vVxbSZLaSnNKPpxppHZnSTlFXd2K5RRpJX0r6+Yx\ndOiQwlqd77nnkhZ4n38OV10FBx64Qgu8Qry2kiQVOks+1O4UWjnFqkokSktLGThwYJOS0VavDX/z\nTTjkEBg2DE46CV59FQ46aKX9pAvh2hZybXxb6YyvWZI6EhNqtTulpaVUVo6huLickpIBFBeXU1k5\nJpUR1Gw2S0XFCOrqxjFr1kvU1Y2jomIEkyZNalaC1Kr1y9OmJR07Bg2CPfaAt96CE06Arl0bfEra\n17Yz1m93xtcsSR2NNdRqtwph0ZTq6mr22quCurqJS7cVFWXo0mU2a665BQsW1DS6drrV6pdnzoRr\nroHKyqSn9LnnQo8eTXpdaVzbzli/3RlfsyQVOtvmqVNpTjlFa1tnnXWoq/sP/y2RGM/ChVnmz396\nmRHrxoxUt7jV3rx5ySTDrbeG2bPhtdfgyiubnExD869tS0oX2k2rwVbUGV+zJHVEqSfUIYSaEMKr\nIYSXQwj/TjsetS9p157+4Q9/BBYDuwBbAgcAm9GcBKnZ9ctffQW33pr0kq6uhmefhf/3/6B372a8\nouZraelCIdRv51tnfM2S1BGlnlCTZCODYow7xBj/J+1g1H6kXXuazWa56qqfA/8GaoDLSP6Xep/m\nJEhNrl+OER58EL75TbjnHnjwQbI330z17Nl5v8FoqJa8KXGkXb+dhs74miWpI0q9hjqE8C6wU4zx\n01U8xhpqLaMQak+rq6sZPHg4s2a9VG/rlhx55E488sjfmt1/ulH1y08/nbTA+/LLpF56n32ouvc+\nKipG0L17WZNqt1vDyq5FSckAnnzyFgYOHNikYxVCbXy+dcbXLEmFqjk11IWQUP//9u49Os76vvP4\n++uLsGrXLCQTkuUikSWN0ywE28cNlxBsihvS9iQlF8A5ac3W4Zh1YAnpJlC2OTjBJQ7QEBaOs4a4\njeUfgvUAABeUSURBVEmCMGmBXNpdDARDsgdi1ZhAAYMhkbjjyYYCJrIs27/9Y0ZCkkeX0Yz0zGje\nr3N8JD96ZvTT5Mnw0dff5/v7JfDvwF7g+pTSDSXOMVBrgGoGuLEaLtQDVQtIA8LWCy8UNmXZtg0u\nuwyWLIEpUzL/BSPr7y9JUrXU68YuJ6aUXoyIHHBnRDyeUvrZ4JNWrlzZ9/nChQtZuHDhxK1QNWdg\n72khwE1072nvP9cvW7ZoQDW6N0BWI0j27rZ41LR3cPFvt3P6rGaaL7sMbr8dmpr6zst6Q5aRXgtJ\nkmrVpk2b2LRpU0XPkXmFur+IuBR4PaX09UHHrVBrP7Wytfd4/XN9Pp9n/hG/x+d3/Ql/zv/mWs5g\nzYwNPPrME/t9n1qpENu6IEmqd3VXoY6I3wGmpJR2RsRM4I+AL2e5JtWPSrf2rlb4y+Vy1Q+PO3fS\n/aUvsbX7dW7iIH6fx9jBIcxu+nnJqnOtVIjH5bWQJKnGZVqhjogjgduARCHcfy+ltLrEeVaoVVW9\n1e0sbuAb1u7dhRF4q1ax64QTmP/Pd/NY932Mtuo80i8JVpAlSRpeXd6UOBoGalVTrbRHDLBvH9xy\nC/zN38BRR8FXvwpz51a1raVmf4mQJKmGGKilUaiFCSED3HknXHwxTJ1aGIF3yikDvlyNqnJN/hIh\nSVINqrseaikLtTAhBIB//ddCkH7mmcIW4Z/4BMT+//8dqi85n8+zdetWAObOnUsulxsyfGc9BUSS\npMmsFnZKlCZE7zblQLa70z31FJx5JnzkI/DJT8KjjxY+lgjTQ2lr28Bhh72LD33os3zoQ6dz6KHv\n5PzzPzfkzpHV2uI6663eJUmqRQZqNYTB25QDdHZu46671tLZuW1ieolfeglWrIDjjoNjjoHt22H5\ncpg+vayn6d3me/fu+4DtwP309EzluuuuH3Lr72pscZ31Vu+SJNUqe6g16WXeP/zaa3DllbBmDZx9\ndmGnw7e+dcxP197ezqJF5/DGGw/1O/puCsNynuw7UqovvFRLyGh6tDN/DSVJmiBj6aG2Qq1Jr7d/\nuBAEoX//8Ljq7oZvfAPe9S549ll48EH4u7+rKEzn83leeeUV9u7tpH/7BrwMPMdILR25XI4FCxb0\nheDRVp3H8zW0jUSSVO8M1Jr0qtU/PGp798J3vgNz5sDdd8Ndd8G3vw0tLfudWk6Y7A2/Z5zx1+zb\nl5g69XjgKOB4pk3bwyc/+ZGyWjp6W0eGahPpb7xeQ9tIJEmTgYFadWu0YbQa/cOjkhL8y7/AvHnw\nzW/CjTfCj34ERx9d8vRywuTg8Lt79300Nc1gw4bLueiiC5g+/QA2btxOSvv4whc+Maq+8HKqzuPx\nGpYT6CVJqmkppZr/U1im9Kabbro5NTcfnA48cF5qbj443XTTzSM+ZseOHWnz5s1px44d1V/Q/fen\n9MEPpvSe96R0220p7ds34lqamw9O8ItUSOK/SM3NBw+5ts2bN6cDD5xXPLfwZ/bsuemOO+4o63kq\nWUPvY6r1Gg71M23evLni55YkaayKubOsrGqFWnVnrJXNwf3DVbFtG3zsY4Wxd0uXkr/7btoPPZT8\nr3897MPK7UkequUCGHNv81iqztV8DSe8FUeSpHFioFbdyewmw/6efx7OOQdOOgmOPx6efJK25pm0\n/Kf/PKoWjnLD5FDhd+7cuRWF0iVLzpz48YFFE9aKI0nSOHNsnupOOSPcqrFt9wCvvFLYHvxb3yoE\n6osugoMOGtNYuba2DSxbtoLp01vo6elk3bo1IwbaUj/PWJ6nllT9fyNJkiowlrF5BmrVpdGEyN5z\nmpoK1eCKgmZXF1x3HVxxBZx+Olx6KRx6aN+X29vbWbz4XF59dUvfsVJzoAerVpg0lEqSVB0GajWU\n4ULkSBXjUQfQPXtg/XpYuRIWLIDLLy+MwyuxlvHa+MSwLEnSxHFjFzWU4W6QG67PelTj6lKC228v\nbBF+443w/e/DrbeWDNO9axmPfmDnNEuSVPusUGtSGqpivGXLz5g//wP7Hb/99jbmzp1bCMD33QcX\nXww7dxb6pT/8YYjR/aJazWqy231LkjTxxlKhnjZei5Gy1FsxXrZs0YA+6507d9LU1EpX15uV666u\ngzj99BXM6XmJW+e8k5bXXoPLLoNPfQqmTi35/EMF51wuV7Ww21tl77/W3iq7gVqSpNphhVqT2uDg\nW6rqewQn8hW6OY3EVwnee+03OOe8FUM+Z1Vvdhxh7VaoJUmaWN6UKI2grW0DS5d+hp6efbyFt3EJ\nz7GUPazhHK7iSl6jkwMOOJlnn32yZGid6JBb7yPxJEmqN7Z8SMPo3WFxes+dfIEfciHXcguJ9/J7\nvMz1xbOOoampdci2ioluw1iy5ExOPfUUp3xIklTDnPKhupXP52lvbx9xy/FenU89xfI0kyf5OEfz\nS45jK381Yw4v00n/nQb37HlmyJ0Gs9gue1y2TJckSVVjoFZdKmucXEpwyy0c++lP86e7X+SjXMUS\nbuZpfkvEi1x55eUccMDJ/O7vzh1x3J3bZUuSpMHsoVbdKauP+Sc/KWwPvm8frF5N269/U7Inudxx\nd262IknS5GQPtRrCqPqYt24tzJJ++mlYtQrOOAOmTGEJlOxJLnfcXTXH40mSpPpmhVp1Z9gK9Wuv\nwZe+BPfcU/j4mc9AU9O4rsVKtSRJk4dbj6shlOpj/t7XLyf3la/A+98P73kPbN8OK1aUFabLvcnR\nbcElSRJYoVYdy+fzPPPoo8z58Y+Z+Q//AH/xF3DJJTCGSnG5m7W46YokSZOTFWo1jr17yd18M/PP\nOouZO3bAli1w9dVjCtO986m7uu7h1Ve30NV1D8uWrRi2Ut3bx10I09C/j1uSJDUWb0pUfZoyBZ5/\nHjZuhGOOGfn8YYxls5aB86gLFerxnkctSZJqkxVq1acIWL264jANY9usxXnUkiSplz3UqnvVmLTR\n20M9eD71RHxvSZJUO8bSQ22gVl0b6mbCsQRdw7EkSTJQq6EMNWnj6qtXc+GFF5c1sWNwkDZcS5LU\nmAzUaijt7e0sXnwur766pe/YrFlH09PzHN3d9zKacXaDK9yXXPJX5HK5sgK5JEmaPAzUaiilKtQH\nHHASEUewa9cjfec1Nx/Nvff+PQsWLBjx8XA8sA/4MvBFnC8tSVJjcQ61GkqpSRurVl3Krl1P039i\nR1fX08yaNWu/x5eaJQ3vBtYBXwPyOF9akiSNxDnUqmtLlpzJqaee0tfv3NHRQXPz2+nqWgS0AJ3M\nmHEIO3fu3O+xpWZJQyewGDgM6ABedL60JEkaloFadS+Xyw1qx3gV+CdgJvAGER8vGYh7K9zLli2i\nq+sg4DfAN4EXge3MmvWX7N37gvOlJUnSsOyh1qRT7kzpfD7P2rU38Ld/eyVNTUfS09PJ1VevZt68\nY0c95cOpIJIkTQ7elCgVTeQc6qFmYUuSpPpjoJbGwXBBe6hZ2E4FkSSpPjnlQ6qytrYNtLTMYfHi\nc2lpmUNb24YBXy81KcSpIJIkNRYr1NIQRlN9tkItSdLkYoVaGkY+n2fjxo1s3LiRfD4/4vmjqT6X\nmoVdjakg+Xye9vb2Ua1TkiRlywq1GkJb2wbOPns5u3fngBeYPn0K69d/a8TpH4Xq85sj+JqbP16y\n+lzNKR/e5ChJUna8KVEqofQW4wuZMSPxzDNPDhuAzz//c1x33fXA4cCznHfeOVx77TUTulZbSCRJ\nmji2fEgldHR0MGXK4QzcYryVqVPfNuzNg/l8nnXrvgM8ADwBPMC6dd8d1zYMb3KUJKn+GKg16bW2\ntrJv37MUKtMUP3awd+8OXnnllSEDcjnhtlo9zwO3Qy+s1a3PJUmqbQZqTXq5XI6rr17NtGknAEcC\nxzN1ajd79+7hjDP+uuQ4PBh9uB1ptF65ax2PmxwlSdL4sYdadW+kGwLXrr2BCy74ItOnt9LT08Hy\n5Uu5/vr17Np1LyP1KY+0jfl49Ty7lbkkSdmwh1oNZ6Tq8Nq1N3DuuRfQ3X0vO3dupbv7XtauXc/0\n6f17qt/BlClvZevWrfs9/5IlZ9LZuY277lpLZ+e2/aZtjFfPcy6XY8GCBYZpSZLqgBVq1a2RqsP5\nfJ7DDz+K7u4jgYf6Hjdr1rH09PyK7u6fAo8D/xV4C83Nvyl7RJ1TOSRJmlysUKuhjFQdLny9BRh4\nQ2JPTyfXXHMVM2acDPwlsAnYTlfXPSxbtqKsGwuH63l2cxZJkhqDgVp1a/+bBjfR3f00s2bN6vv6\nnj3PAxcBi4D3AcdxzTVXsHz5OfzgBxuYOfNdVNquUaotpJo3KkqSpNpmy4fqWu9NgykdyK5dL9Hc\nfBTwfF/rRu/Xp079j/T0PMOqVZdy8skn9U3qGK8bCuu9DcSbIiVJjaoud0qMiNOAb1Colq9LKX2t\nxDkGag3p8ccfZ+7cE+juLj21ozccPvjgQ1x44cUDtvQGhp3iMRbt7e0sXnwur766pe/Y7NnzuOuu\ntSxYsKCi554Ibn0uSWpkdReoI2IK8CTwh8ALQDtwVkpp26DzDNQa0mgC7HBVY6Cq1dh6rlDX89ol\nSaqGerwp8Q+A7SmlzpRSD3Az8NGM16Q6M5oNWIa7gbHaI+rqeXMWtz6XJKl80zL+/odSGMHQ6zkK\nIVsatd4Au2zZogGtG/0D7MDQXai8jueW3kuWnMmpp55Sd33IE/06SZI0GWQdqEdt5cqVfZ8vXLiQ\nhQsXZrYW1Z6RAuxoQne15XK5ugnSvbJ4nSRJytKmTZvYtGlTRc+RdQ/1ccDKlNJpxb9fDKTBNyba\nQ61qcXrF6Pg6SZIaVT3elDgVeILCTYkvApuBJSmlxwedZ6CWJEnSuBtLoM605SOltDcizgM28ubY\nvMdHeJgkSZJUMzKfQz0aVqglSZI0EepxbJ4kSZJU1wzUkiRJUgUM1Jo08vk87e3t5PP5rJciSZIa\niIFak0Jb2wZaWuawePG5tLTMoa1tQ9ZLkiRJDcKbElX38vk8LS1z6Oq6h97d/ZqbF9HZuc0ZypIk\nqSzelKiG1NHRQVNTK4UwDXAM06e30NHRkd2iJElSwzBQq+61traye3cH8HDxyMP09HTS2tqa3aIk\nSVLDMFCr7uVyOdatW0Nz8yJmz55Hc/Mi1q1bY7uHJEmaEPZQa9LI5/N0dHQwa9Ysdu7cSWtrq6Fa\nkiSVxR5qNbRcLsdTT/2S+fM/4LQPSZI0YaxQa9LIctpHb3XcqrgkSfXNCrUaWlbTPpyBLUlSY7NC\nrUkjiwq1M7AlSZpcrFCroWUx7cMZ2JIkyQq1Jp2J7Ge2Qi1J0uQylgr1tPFajJSVXC43YWG2tyq+\nbNkipk9voaen0xnYkiQ1GCvUUhU45UOSpMlhLBVqA7UkSZJU5E2JkiRJ0gQzUEuSJEkVMFBLkiRJ\nFTBQS5IkSRUwUEuSJEkVMFBLkiRJFTBQS5IkSRUwUEuSJEkVMFCrbuXzedrb28nn81kvRZIkNTAD\ntepSW9sGWlrmsHjxubS0zKGtbUPWS5IkSQ3KrcdVd/L5PC0tc+jqugc4BniY5uZFdHZuI5fLZb08\nSZJUx9x6XA2ho6ODpqZWCmEa4BimT2+ho6Mju0VJkqSGZaBW3WltbWX37g7g4eKRh+np6aS1tTW7\nRUmSpIZloFbdyeVyrFu3hubmRcyePY/m5kWsW7fGdg9JkpQJe6hVt/L5PB0dHbS2thqmJUlSVYyl\nh9pALUmSJBV5U6IkSZI0wQzUkiRJUgUM1JIkSVIFDNSSJElSBQzUkiRJUgUM1JIkSVIFDNSSJElS\nBQzUkiRJUgUM1JIkSVIFDNSSJElSBQzUkiRJUgUM1JIkSVIFDNSSJElSBQzUkiRJUgUM1JIkSVIF\nDNSSJElSBQzUkiRJUgUM1JIkSVIFDNSSJElSBQzUkiRJUgUM1JIkSVIFMgvUEXFpRDwXEQ8W/5yW\n1VpUnzZt2pT1ElSDvC5UiteFSvG6ULVkXaH+ekppXvHP/8l4LaozvhGqFK8LleJ1oVK8LlQtWQfq\nyPj7S5IkSRXJOlCfFxEPRcS3IuLAjNciSZIklS1SSuP35BF3Aof0PwQk4H8ADwC/TimliFgFvCOl\ntGyI5xm/RUqSJEn9pJTK6qIY10A96kVEtAA/Sikdk/VaJEmSpHJkOeXj7f3++jHg37JaiyRJkjRW\n0zL83ldExLHAPqADWJ7hWiRJkqQxqYmWD0mSJKleZT3lY1gRcVpEbIuIJyPioqzXo9oQER0R8YuI\n2BoRm7Nej7ITEesi4uWIeLjfsYMiYmNEPBERdzhBqLEMcU24kViDi4jDIuInEfFoRDwSEf+teNz3\niwZW4ro4v3i87PeMmq1QR8QU4EngD4EXgHbgrJTStkwXpsxFxC+B+SmlV7Jei7IVER8AdgI39t7U\nHBFfA/5fSumK4i/iB6WULs5ynZo4Q1wTlwKvp5S+nunilJnifVtvTyk9FBGzgC3AR4H/gu8XDWuY\n6+JMynzPqOUK9R8A21NKnSmlHuBmCj+kFNT2tasJklL6GTD4F6uPAuuLn68H/mxCF6VMDXFNgBuJ\nNbSU0ksppYeKn+8EHgcOw/eLhjbEdXFo8ctlvWfUcig5FHi239+f480fUo0tAXdGRHtEnJP1YlRz\n3pZSehkKb5bA2zJej2qDG4kJgIhoBY6lsB/GIb5fCAZcFz8vHirrPaOWA7U0lBNTSvOAPwY+W/wn\nXmkotdnXpom0BnhnSulY4CXA1o8GVfxn/X8ELihWJAe/P/h+0YBKXBdlv2fUcqB+Hjii398PKx5T\ng0spvVj8mAduo9AeJPV6OSIOgb7+uB0Zr0cZSynl05s3DN0ALMhyPcpGREyjEJq+k1L6QfGw7xcN\nrtR1MZb3jFoO1O3AURHREhFNwFnADzNekzIWEb9T/E2SiJgJ/BFuCtTogoG9bj8Ezi5+vhT4weAH\naNIbcE24kZiK/h54LKV0Tb9jvl9ov+tiLO8ZNTvlAwpj84BrKAT/dSml1RkvSRmLiCMpVKUThY2J\nvud10bgi4iZgIfAW4GXgUuB24PvA4UAncEZK6d+zWqMm1hDXxCIKvZF9G4n19s2qMUTEicB9wCMU\n/vuRgEuAzcAt+H7RkIa5Lj5Fme8ZNR2oJUmSpFpXyy0fkiRJUs0zUEuSJEkVMFBLkiRJFTBQS5Ik\nSRUwUEuSJEkVMFBLkiRJFTBQS9IEi4i9EfFgRDwSERsiYkaVn39pRFw7wjknR8Tx/f6+PCI+Xc11\nSFKjMFBL0sR7I6U0L6V0NNADnDsO32OkTQYWAif0nZzS2pTSd8dhHZI06RmoJSlbPwWOAoiIzxer\n1g9HxAXFYy0R8XhEfDciHouIW3or2hHxq4g4uPj5/Ii4Z/CTR8SfRsQDEbElIjZGRC4iWiiE+M8V\nK+UnRsSlEfH54mOOjYj7I+KhiPiniDiwePyeiFgdET+PiG3FXcYkqeEZqCVp4gVAREwDPgw8EhHz\ngKXAAuB44JyIeF/x/HcD16WUfh94HVhRPD64Cl2qKv3TlNJxKaX5wAbgiymlTuB/AVcXK+X/d9Bj\n1gNfSCkdC/wbhe27e01NKb0fuBBYWebPLUmTkoFakiZec0Q8CGwGOoB1wAeA21JKu1JKbwC3AicV\nz38mpfRA8fPvFs+FYjAfweERcUdEPAz8d+C9w50cEbOBA1NKPyseWg98sN8ptxY/bgFaRvH9JWnS\nm5b1AiSpAf02pTSv/4GI0WTjPr2V6D28WRgZ6sbGa4GrUkr/HBEnM7DaPJThFtNd/LgX/xsiSYAV\naknKQqnA+lPgzyJiRkTMBE4vHgM4IiLeX/z8U/2O/wqYX/z840N8r9nAC8XPl/Y7/nrxawOklF4D\nftOvP/rPgXvL+DkkqeEYqCVp4u3X65xS2gp8G2gH7geuTyn9ovjlJ4DPRsRjwH+g0P8M8BXgf0bE\nZgrV6lK+DPxjRLQD+X7HfwSc3ntT4qA1nQ1cFREPAe8rfp9S6x5pkogkNYRIyfdDSapVxYkcPy6O\n2JMk1SAr1JJU+6x8SFINs0ItSZIkVcAKtSRJklQBA7UkSZJUAQO1JEmSVAEDtSRJklQBA7UkSZJU\ngf8PuUExisiH0mQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedd8b07fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(data.Population.min(), data.Population.max(), 100)\n",
    "f = final_W[0, 0] + (final_W[0, 1] * x)\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(x, f, 'r', label='Prediction')\n",
    "ax.scatter(data.Population, data.Profit, label='Traning Data')\n",
    "ax.legend(loc=2)\n",
    "ax.set_xlabel('Population')\n",
    "ax.set_ylabel('Profit')\n",
    "ax.set_title('Predicted Profit vs. Population Size')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fedd89e1050>"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XcuxIBY4WV9pB/pFSWqvyeFvg5JTSHlX7nA3cklL6Q+Xx48DIlNLLnY6V0uWXw777Flav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\nQQzbkiRJUkEM25IkSVJBDNuSJElSQf4/GIiVqqJxnIQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedd8a9c850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(np.arange(iters), cost, 'r')\n",
    "ax.set_xlabel('Iterations')\n",
    "ax.set_ylabel('Cost')\n",
    "ax.set_title('Error vs. Training Epoch')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression with multiple variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# predicting housing price from size of the house in square feet and number of bedrooms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Size</th>\n",
       "      <th>Bedrooms</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2104</td>\n",
       "      <td>3</td>\n",
       "      <td>399900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1600</td>\n",
       "      <td>3</td>\n",
       "      <td>329900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>3</td>\n",
       "      <td>369000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1416</td>\n",
       "      <td>2</td>\n",
       "      <td>232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>4</td>\n",
       "      <td>539900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Size  Bedrooms   Price\n",
       "0  2104         3  399900\n",
       "1  1600         3  329900\n",
       "2  2400         3  369000\n",
       "3  1416         2  232000\n",
       "4  3000         4  539900"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = pd.read_csv('data/linear_Reg_2.txt', header=None, names=['Size', 'Bedrooms', 'Price'])\n",
    "data2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13070336960771892"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = (data2 - data2.mean()) / data2.std()\n",
    "\n",
    "# add ones column\n",
    "data2.insert(0, 'Ones', 1)\n",
    "\n",
    "# set X (training data) and y (target variable)\n",
    "cols = data2.shape[1]\n",
    "X2 = data2.iloc[:,0:cols-1]\n",
    "y2 = data2.iloc[:,cols-1:cols]\n",
    "\n",
    "# convert to matrices and initialize theta\n",
    "X2 = np.matrix(X2.values)\n",
    "y2 = np.matrix(y2.values)\n",
    "W2 = np.matrix(np.array([0,0,0]))\n",
    "\n",
    "# perform linear regression on the data set\n",
    "final_W2, cost2 = gradientDescent(X2, y2, W2, alpha, iters)\n",
    "\n",
    "# get the cost (error) of the model\n",
    "computeCost(X2, y2, final_W2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fedae25f5d0>"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xfHvK7ruXXY0kSZLaRFNbU0ZLqa0pAD/7GZx1Flx44dDrSpIkqS01ujXFIN4I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\nSSrB/wf4ekd5z/XXGgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedae2ae0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(np.arange(iters), cost2, 'r')\n",
    "ax.set_xlabel('Iterations')\n",
    "ax.set_ylabel('Cost')\n",
    "ax.set_title('Error vs. Training Epoch')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# do it in a simple steps - Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "model = linear_model.LinearRegression()\n",
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fedae22b910>"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XAGb5AAAAyLUHH/SCc0eY/uADb6SaMF0SCNQAAAApxGIxNTU1KRaLpX+QFSu8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedd8b39f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array(X[:, 1].A1)\n",
    "f = model.predict(X).flatten()\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(x, f, 'r', label='Prediction')\n",
    "ax.scatter(data.Population, data.Profit, label='Traning Data')\n",
    "ax.legend(loc=2)\n",
    "ax.set_xlabel('Population')\n",
    "ax.set_ylabel('Profit')\n",
    "ax.set_title('Predicted Profit vs. Population Size')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.19303364]])"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.89578088])"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistics Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# predict whether a student gets admitted to a university"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exam 1</th>\n",
       "      <th>Exam 2</th>\n",
       "      <th>Admitted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Exam 1     Exam 2  Admitted\n",
       "0  34.623660  78.024693         0\n",
       "1  30.286711  43.894998         0\n",
       "2  35.847409  72.902198         0\n",
       "3  60.182599  86.308552         1\n",
       "4  79.032736  75.344376         1"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/log_Reg_1.txt', header=None, names=['Exam 1', 'Exam 2', 'Admitted'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fedae145fd0>"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JbgjyCpJAoPl5lUMmewHlFZbJx2FXDZ+T366mYmy0/gMmKSxt9gCMjd7vwRD2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedae21eb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "positive = data[data['Admitted'].isin([1])]\n",
    "negative = data[data['Admitted'].isin([0])]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.scatter(positive['Exam 1'], positive['Exam 2'], s=50, c='b', marker='o', label='Admitted')\n",
    "ax.scatter(negative['Exam 1'], negative['Exam 2'], s=50, c='r', marker='x', label='Not Admitted')\n",
    "ax.legend()\n",
    "ax.set_xlabel('Exam 1 Score')\n",
    "ax.set_ylabel('Exam 2 Score')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create a sigmoid function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedae10f150>]"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6oQXadYwBBtE55yS/8ztCMcAogjHAIBoeTo47ru0qALqKUQqAQfPLXya77NKMUay7btvV\nAEwJoxQAjO3cc5MjjxSKAZYjGAMMGqtRAKyQUQqAQfLAA8mLXpTcdVey4YZtVwMwZYxSALBq55+f\nvOY1QjHACgjGAINkzhxjFAArYZQCYFA8/HCy7bbJHXckL3hB29UATCmjFACs3De/mbzqVUIxwEoI\nxgCDwmoUAKtklAJgEDz+eLL11skttySbb952NQBTzigFACt2ySXJK14hFAOsgmAMMAiMUQCMySgF\nQL978slkq62SuXObe4ABYJQCgOf71reSvfYSigHGIBgD9DtjFADjYpQCoJ8tWtR0in/0o2T77duu\nBmDaGKUA4LlGRpKddhKKAcZBMAboZ8YoAMZtXMG4lHJkKeWmUsrNpZSPrOSYoVLKj0opPy2lfLuz\nZQIwYYsXJ+eeKxgDjNOaYx1QSpmR5OQkhyW5O8l1pZTzaq03jTpmkySnJHltrfWuUooV5AHa9l//\nlWy5ZTJrVtuVAPSE8XSM908yv9Z6e611UZKvJzl6uWPenGS41npXktRa7+9smQBM2PBwctxxbVcB\n0DPGE4xnJrlz1PMFS18bbZckv1VK+XYp5bpSyts6VSAAk7BkSXL22cYoACZgzFGKCZxnvySvSbJB\nkmtKKdfUWn++/IGzZ89+5vHQ0FCGhoY6VAIAz7juumTDDZM99mi7EoBpMTIykpGRkdU6x5jrGJdS\nDkwyu9Z65NLnf5Gk1lo/PuqYjyRZt9b6t0ufn5Hk4lrr8HLnso4xwHT48IeTtddOPvrRtisBaMVU\nrWN8XZJZpZQdSilrJzk+yfnLHXNekleVUtYopayf5IAkcydSCAAdUqtl2gAmYcxRilrr4lLK+5Jc\nliZIn1lrnVtKOaF5u55Wa72plHJpkuuTLE5yWq31ximtHIAV+/GPm3C8zz5tVwLQU2wJDdBv/vqv\nkyefTD75ybYrAWiNLaEBMEYBMEmCMUA/ufHG5JFHkv33b7sSgJ4jGAP0k+Hh5Nhjkxm+3gEmyjcn\nQD8xRgEwaYIxQL+45ZbknnuSV72q7UoAepJgDNAvhoeTN7whWWONtisB6EmCMUC/MEYBsFqsYwzQ\nD+68M9l332aUYq212q4GoHXWMQYYVGefnfzu7wrFAKtBMAboB3PmGKMAWE1GKQB63b33Jrvtltx3\nX7LOOm1XA9AVjFIADKJzzkmOOkooBlhNgjFAr7MaBUBHGKUA6GW//nXy4hcnd9+dbLBB29UAdA2j\nFACD5rzzksMPF4oBOkAwBuhlxigAOsYoBUCveuihZLvtkgULko03brsagK5ilAJgkFx4YXLIIUIx\nQIcIxgC9yhgFQEcZpQDoRY8+mmyzTXLbbclv/Vbb1QB0HaMUAIPi4ouTAw8UigE6SDAG6EXGKAA6\nzigFQK9ZuDDZaqtk3rxkyy3brgagKxmlABgEl12W7L23UAzQYYIxQK8ZHk6OO67tKgD6jlEKgF7y\n1FPJ1lsn11+fzJzZdjUAXcsoBUC/+/a3k112EYoBpoBgDNBLrEYBMGWMUgD0iqefbjb1+O//Tnbc\nse1qALqaUQqAfvad7yTbbisUA0wRwRigVxijAJhSRikAesGSJU23+Mork912a7sagK5nlAKgX33/\n+8mmmwrFAFNIMAboBcYoAKbcmm0XAMAYam2C8XnntV0JQF/TMQbodj/8YbLWWslLX9p2JQB9TTAG\n6HbLxijKhK4hAWCCBGOAbrZsjMJ8McCUE4wButnPfpYsXJi8/OVtVwLQ9wRjgG42PJwce6wxCoBp\nIBgDdLM5c4xRAEwTwRigW918c3L//clBB7VdCcBAEIwButXwcPKGNyQzfFUDTAfftgDdymoUANOq\n1Fqn78NKqdP5eQA967bbmpUo7r03WdMmpQATVUpJrXVCVy7rGAN0o7PPTo45RigGmEaCMUA3MkYB\nMO2MUgB0m7vvTvbaqxmjWHvttqsB6ElGKQD6wTnnJK9/vVAMMM0EY4BuY4wCoBVGKQC6ya9+lcya\n1YxRrLde29UA9CyjFAC97txzkyOOEIoBWiAYA3QTYxQArTFKAdAtHngg2WGH5K67ko02arsagJ5m\nlAKgl11wQXLooUIxQEsEY4BuMTycHHdc21UADCyjFADd4JFHkpkzkzvuSF7wgrarAeh5RikAetVF\nFyW//dtCMUCLBGOAbmA1CoDWGaUAaNvjjydbb538/OfJFlu0XQ1AXzBKAdCLLr00ednLhGKAlgnG\nAG0zRgHQFYxSALTpySeTrbZKfvazZJtt2q4GoG8YpQDoNVdckeyxh1AM0AUEY4A2GaMA6BpGKQDa\n8vTTzRjFD36QvOhFbVcD0FeMUgD0kquuSnbcUSgG6BKCMUBbjFEAdBWjFABtWLIkmTkzufrqZOed\n264GoO8YpQDoFd/7XrOhh1AM0DUEY4A2GKMA6Dprtl0AwMCptQnGF13UdiUAjKJjDDDdrrsuWW+9\nZM89264EgFEEY4DptmyMokzomhAApphgDDCdlo1RmC8G6DqCMcB0uv76ZPHiZL/92q4EgOUIxgDT\nyRgFQNcSjAGmkzEKgK4lGANMl5tuSh58MDnggLYrAWAFBGOA6TI8nBx7bDLDVy9ANxrXt3Mp5chS\nyk2llJtLKR9ZxXGvKKUsKqUc27kSAfqEMQqArjZmMC6lzEhycpIjkuyZ5A9KKbut5LiPJbm000UC\n9Lxbb00WLEgOPrjtSgBYifF0jPdPMr/WenutdVGSryc5egXHvT/JnCS/7GB9AP1heDg55phkjTXa\nrgSAlRhPMJ6Z5M5Rzxcsfe0ZpZRtkhxTa/1cEmsQASzPGAVA11uzQ+f55ySjZ49XGo5nz579zOOh\noaEMDQ11qASALrVgQXLzzcmhh7ZdCUDfGhkZycjIyGqdo9RaV31AKQcmmV1rPXLp879IUmutHx91\nzK3LHibZPMljSd5baz1/uXPVsT4PoO989rPJ//xPctZZbVcCMDBKKam1TmiSYTyjFNclmVVK2aGU\nsnaS45M8J/DWWl+89LZjmjnjP10+FAMMrOHh5Ljj2q4CgDGMOUpRa11cSnlfksvSBOkza61zSykn\nNG/X05b/kSmoE6A33Xdf8pOfJIcf3nYlAIxhzFGKjn6YUQpg0HzhC8nISPK1r7VdCcBAmapRCgAm\ny2oUAD1DxxhgqvzmN8mOOyZ3351ssEHb1QAMFB1jgG5y/vnJYYcJxQA9QjAGmCpz5hijAOghRikA\npsLDDyfbbpvceWeyySZtVwMwcIxSAHSLCy9MDj5YKAboIYIxwFSwGgVAzzFKAdBpjz2WbLNNcuut\nyWabtV0NwEAySgHQDS65JNl/f6EYoMcIxgCdZowCoCcZpQDopCefTLbaKpk7t7kHoBVGKQDadvnl\nyUteIhQD9CDBGKCTjFEA9CyjFACdsmhR0yn+8Y+T7bZruxqAgWaUAqBN3/52MmuWUAzQowRjgE4x\nRgHQ04xSAHTC4sXNph7f+16y005tVwMw8IxSALTlu99Ntt5aKAboYYIxQCcMDyfHHdd2FQCsBqMU\nAKtryZJk++2bNYx3373tagCIUQqAdlx7bbLxxkIxQI8TjAFWl9UoAPrCmm0XANDTam2C8dlnt10J\nAKtJxxhgdfzoR0kpyd57t10JAKtJMAZYHcvGKMqEru8AoAsJxgCTtWyMwnwxQF8QjAEm68Ybk8ce\nS17xirYrAaADBGOAyRoeTo49NpnhqxSgH/g2B5gsu90B9BXBGGAyfv7z5L77koMOarsSADpEMAaY\njOHh5A1vSNZYo+1KAOgQwRhgMqxGAdB3Sq11+j6slDqdnwcwJe64I9lvv+See5K11mq7GgBWoJSS\nWuuEFpnXMQaYqLPPTn7v94RigD4jGANM1Jw5xigA+pBRCoCJuOeeZI89knvvTdZZp+1qAFgJoxQA\nU+2cc5KjjhKKAfqQYAwwEVajAOhbRikAxuv++5OddmrGKdZfv+1qAFgFoxQAU+m885LXvlYoBuhT\ngjHAeBmjAOhrRikAxuPBB5Ptt0/uuivZaKO2qwFgDEYpAKbKhRcmQ0NCMUAfE4wBxsMYBUDfM0oB\nMJZHH0222Sa5/fZk003brgaAcTBKATAVLrooeeUrhWKAPicYA4zFGAXAQDBKAbAqTzyRbLVVMn9+\n8sIXtl0NAONklAKg0y67LNl3X6EYYAAIxgCrMjycHHdc21UAMA2MUgCszFNPNWMUN9yQzJzZdjUA\nTIBRCoBOuvLKZLfdhGKAASEYA6yM1SgABopRCoAVWbgw2W675Nprkx13bLsaACbIKAVAp5xxRnLg\ngUIxwADRMQZY3sKFyaxZybnnJi9/edvVADAJOsYAnXDGGc3axUIxwEDRMQYYTbcYoC/oGAOsrtNP\n1y0GGFA6xgDLLFyY7LRTcv75ycte1nY1AKwGHWOA1XH66U0gFooBBpKOMUCiWwzQZ3SMASbrtNN0\niwEGnI4xwBNPNCtRXHBBst9+bVcDQAfoGANMxumnN6tQCMUAA03HGBhsusUAfUnHGGCidIsBWErH\nGBhcTzzRrERx4YWCMUCf0TEGmIjTTkv2318oBiCJjjEwqJZ1i7/5zWYLaAD6io4xwHgt6xYLxQAs\npWMMDB7dYoC+p2MMMB5f+EJywAFCMQDPoWMMDBbdYoCBoGMMMBbdYgBWQscYGBy6xQADQ8cYYFU+\n/3ndYgBWSscYGAyPP950iy++ONlnn7arAWCK6RgDrMwXvpC88pVCMQArpWMM9D/dYoCBM2Ud41LK\nkaWUm0opN5dSPrKC999cSvnJ0tt3SykvmUgRAFNKtxiAcRizY1xKmZHk5iSHJbk7yXVJjq+13jTq\nmAOTzK21PlRKOTLJ7FrrgSs4l44xML2WdYsvuSTZe++2qwFgmkxVx3j/JPNrrbfXWhcl+XqSo0cf\nUGv9fq31oaVPv59k5kSKAJgyn/98ctBBQjEAY1pzHMfMTHLnqOcL0oTllXl3kotXpyiAjnj88eST\nn2y6xQAwhvEE43ErpRya5B1JXtXJ8wJMim4xABMwnmB8V5LtRz3fdulrz1FKeWmS05IcWWt9YGUn\nmz179jOPh4aGMjQ0NM5SASbgsceabvGll7ZdCQDTYGRkJCMjI6t1jvFcfLdGknlpLr67J8m1Sf6g\n1jp31DHbJ7kiydtqrd9fxblcfAdMj3/8x+Saa5I5c9quBIAWTObiu3GtY7x0pYnPpLlY78xa68dK\nKSckqbXW00oppyc5NsntSUqSRbXW580hC8bAtHjssWYlissuS1760rarAaAFUxaMO0UwBqaFbjHA\nwBOMAXSLAcgU7nwH0DM+97nk4IOFYgAmTMcY6B/LusWXX568xM70AINMxxgYbMu6xUIxAJOgYwz0\nB91iAEbRMQYG16mn6hYDsFp0jIHe99hjyYtfnFxxRbLXXm1XA0AX0DEGBtOppyaHHCIUA7BadIyB\n3qZbDMAK6BgDg0e3GIAO0TEGetejjzYrUegWA7AcHWNgsJx6ajI0JBQD0BE6xkBv0i0GYBV0jIHB\noVsMQIfpGAO9Z1m3+Morkz33bLsaALqQjjEwGE45JTn0UKEYgI7SMQZ6i24xAOOgYwz0P91iAKaI\njjHQO5Z1i7/97WSPPdquBoAupmMM9LeTT05e8xqhGIApoWMM9IZHHmm6xSMjgjEAY9IxBvrXKack\nhx0mFAMwZXSMge6nWwzABOkYA/3plFOS//W/hGIAppSOMdDdlnWLr7oq2X33tqsBoEfoGAP95+ST\nm26xUAzAFNMxBrqXbjEAk6RjDPQX3WIAppGOMdCdHn44mTUrufrqZLfd2q4GgB6jYwz0j5NPTg4/\nXCgGYNroGAPd5+GHm9ni73xHMAZgUibTMRaMge6yZEny3vcmCxcm//7vbVcDQI+aTDBec6qKAZiw\np59O3vWu5Be/SC68sO1qABgwgjHQHZ56KnnrW5MHH0wuuSRZf/22KwJgwAjGQPsWLkyOOy5ZY43k\n/POTdddtuyIABpBVKYB2PfZY8ju/k2y4YTJnjlAMQGsEY6A9Dz2UHHFEst12yVe+kqy1VtsVATDA\nBGOgHb/+dbOr3T77JGee2YxRAECLBGNg+t13XzI0lBx6aPIv/5LM8FUEQPv8bQRMrwULkle/urnY\n7uMfT8osOTJhAAAJM0lEQVSElpgEgCljVQpg+tx6azM+8ad/mvyf/9N2NQDwHDrGwPS46abkkEOa\nQCwUA9CFdIyBqXf99cmRRyYnnpi8/e1tVwMAKyQYA1PruuuadYo/+9nkTW9quxoAWCnBGJg63/lO\n8sY3Nsux/e7vtl0NAKySYAxMjcsvT9785uSrX00OP7ztagBgTC6+AzrvgguSt7wlOftsoRiAniEY\nA531H/+RvPvdyYUXJgcf3HY1ADBugjHQOWedlXzwg80Yxf77t10NAEyIGWOgM049NTnppOTKK5Pd\ndmu7GgCYMMEYWH2f+lRyyinJVVclL35x29UAwKQIxsDk1Zr83d81K09cfXWy3XZtVwQAkyYYA5NT\na/KRjyQXX9yE4i23bLsiAFgtgjEwcUuWJB/4QPL97ycjI8lmm7VdEQCsNsEYmJjFi5vl2ObPT664\nItlkk7YrAoCOEIyB8Vu0KHnb25L7708uvTTZYIO2KwKAjhGMgfFZuDB505uajvGFFybrrtt2RQDQ\nUTb4AMb2+OPJ7/1esvbazTbPQjEAfUgwBlbt4YeTI49Mttoq+drXmnAMAH1IMAZW7je/SQ4/PNlz\nz+SLX0zWNH0FQP8SjIEV++Uvk0MPTV71qma75xm+LgDob/6mA57vrruSQw5Jjj662e65lLYrAoAp\nJxgDz3XbbcmrX528/e3Nds9CMQADQjAGGnfckfzt3yavfGXywQ822z0DwAARjGGQLVrULL921FHJ\nvvs2c8UXX5y8//1tVwYA084l5jCI5s9PzjgjOeusZJddmi2e58xJ1l+/7coAoDWCMQyKJ55ousOn\nn57MnZv84R8mIyPJbru1XRkAdAXBGPrd9dc33eGvfjV5+cuT973v2V3sAIBnCMbQjx55JPnGN5ru\n8N13J+98Z/KDHyQvelHblQFA1yq11un7sFLqdH4eDJRak2uvbcLw8HAyNJS85z3JEUcka6zRdnUA\nMK1KKam1TmjNUR1j6HW/+U3y7//eBOInnmgupJs7N9lqq7YrA4CeomMMvajW5sK5M85IvvnN5PWv\nbwLxIYfYuhkAMrmOsWAMveTee5MvfjE588xk3XWbUYm3vCXZbLO2KwOArmKUAvrR4sXJpZc2oxIj\nI8kb35h8+cvJAQfYrhkAOkgwhm51++3Jv/5rc9t666Y7/KUvJRtt1HZlANCXBGPoJk89lZx/fjM7\nfN11yZvfnFx4YbL33m1XBgB9TzCGtjzySHLzzc1t3rzmduWVye67NxfSnXNOst56bVcJAAPDxXcw\nlRYtSm67rQm9ywLwsvsHH0x23jnZdddkl12a+wMPbF4DAFaLVSmgDbUmv/zls13f0QH4ttua+eBd\nd31uAN5ll2TbbS2tBgBTRDCGqfTYY8n8+Svu/q655orD76xZzbJqAMC0EoxhdS1e3HR5lw++N9+c\n3H9/stNOzw+/u+5qHWEA6DJTFoxLKUcm+eckM5KcWWv9+AqO+WyS1yV5LMnba60/XsExgjHT4+mn\nk4cffvb20EPPvV/+tQceyMj112fovvuSF75wxeF3++2TNdZo+5+MATQyMpKhoaG2y4Dn8btJN5uS\nDT5KKTOSnJzksCR3J7mulHJerfWmUce8LslOtdadSykHJPl8kgMnVD0kyZIlyaOPrjzAjve1hQub\n9X432STZeOPmtqLHW275zPORSy/N0Kc/nay/ftv/FuA5hA+6ld9N+s14lmvbP8n8WuvtSVJK+XqS\no5PcNOqYo5N8KUlqrf9dStmklLJlrfW+ThfMCtTa3JYsGfs2+rjFi5vO6lNPNasnLLufiseren/h\nwmdD7aOPNsF0dHhdUaDdYYfnvzb6uA03nPiucD/5iVAMAANsPMF4ZpI7Rz1fkCYsr+qYu5a+9vxg\nfMQRzf3yIxWrej6RY8f7s8vCZJvPxxNkVxRoV/ReKc0KByu7rez9tdZ69rb22qt+PNb7G2ww9jEr\nerzuus+G2o02Mq4AALRizBnjUsobkxxRa33v0udvTbJ/rfUDo465IMlJtdbvLX3+rSQfrrX+cLlz\nGTAGAGBadHzGOE33d/tRz7dd+tryx2w3xjETLg4AAKbLeHYXuC7JrFLKDqWUtZMcn+T85Y45P8kf\nJkkp5cAkD5ovBgCgl4zZMa61Li6lvC/JZXl2uba5pZQTmrfrabXWi0opR5VSfp5mubZ3TG3ZAADQ\nWdO6wQcAAHSr8YxSrLZSynGllJ+WUhaXUvZb7r2/LKXML6XMLaW8djrqgRUppfxNKWVBKeWHS29H\ntl0Tg62UcmQp5aZSys2llI+0XQ+MVkq5rZTyk1LKj0op17ZdD4OtlHJmKeW+Usr1o17btJRyWSll\nXinl0lLKJmOdZ1qCcZIbkrwhyVWjXyyl7J7k95PsnmbXvFNLmejis9BRn6617rf0dknbxTC4Rm2u\ndESSPZP8QSllt3argudYkmSo1rpvrXX5ZVxhuv1bmu/L0f4iybdqrbsmuTLJX451kmkJxrXWebXW\n+UmWD71HJ/l6rfXpWuttSebn+Wskw3TyH2Z0i2c2V6q1LkqybHMl6BYl09dgg1WqtX43yQPLvXx0\nkrOWPj4ryTFjnaftX+iVbQwCbXlfKeXHpZQzxvO/XGAKrWhzJd+PdJOa5PJSynWllPe0XQyswAuX\nrZJWa703yQvH+oHxrGM8LqWUy5NsOfqlNH9o/qrWekGnPgdWx6p+T5OcmuTvaq21lPLRJJ9O8q7p\nrxKgJ/x2rfWeUsoWaQLy3KVdO+hWY6440bFgXGs9fBI/Nq6NQaBTJvB7enoS/0FHm8azuRK0ptZ6\nz9L7X5VSzkkz/iMY003uK6VsWWu9r5SyVZJfjvUDbYxSjJ7hPD/J8aWUtUspOyaZlcSVrbRi6R+a\nZY5N8tO2aoGMb3MlaEUpZf1SyoZLH2+Q5LXxnUn7Sp6fM9++9PEfJTlvrBN0rGO8KqWUY5L8S5LN\nk1xYSvlxrfV1tdYbSyn/keTGJIuS/Gm1sDLt+UQpZZ80V1rfluSEdsthkK1sc6WWy4JltkxyTiml\npskSX6m1XtZyTQywUspXkwwl2ayUckeSv0nysST/WUp5Z5Lb06yEturzyKEAAND+qhQAANAVBGMA\nAIhgDAAASQRjAABIIhgDAEASwRgAAJIIxgAAkCT5/5wLeGfDtXL+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedae10f290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nums = np.arange(-10, 10, step=1)\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(nums, sigmoid(nums), 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# measuring cost (error)\n",
    "# y = sigmoid(X * W.T)\n",
    "# y - sigmoid(X * W.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cost(W, X, y):\n",
    "    W = np.matrix(W)\n",
    "    X = np.matrix(X)\n",
    "    y = np.matrix(y)\n",
    "    first = np.multiply(-y, np.log(sigmoid(X * W.T)))\n",
    "    second = np.multiply((1 - y), np.log(1 - sigmoid(X * W.T)))\n",
    "    return np.sum(first - second) / (len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# add a ones column - this makes the matrix multiplication work out easier\n",
    "data.insert(0, 'Ones', 1)\n",
    "\n",
    "# set X (training data) and y (target variable)\n",
    "cols = data.shape[1]\n",
    "X = data.iloc[:,0:cols-1]\n",
    "y = data.iloc[:,cols-1:cols]\n",
    "\n",
    "# convert to numpy arrays and initalize the parameter array theta\n",
    "X = np.array(X.values)\n",
    "y = np.array(y.values)\n",
    "W = np.zeros(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 3), (3,), (100, 1))"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, W.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.69314718055994529"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost(W, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# finding the best values of W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradient(W, X, y):\n",
    "    W = np.matrix(W)\n",
    "    X = np.matrix(X)\n",
    "    y = np.matrix(y)\n",
    "    \n",
    "    parameters = int(W.ravel().shape[1])\n",
    "    grad = np.zeros(parameters)\n",
    "    \n",
    "    error = sigmoid(X * W.T) - y\n",
    "    \n",
    "    for i in range(parameters):\n",
    "        term = np.multiply(error, X[:,i])\n",
    "        grad[i] = np.sum(term) / len(X)\n",
    "    \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.1       , -12.00921659, -11.26284221])"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient(W, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-25.16131863,   0.20623159,   0.20147149]), 36, 0)"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.optimize as opt\n",
    "result = opt.fmin_tnc(func=cost, x0=W, fprime=gradient, args=(X, y))\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# prediction for test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predict(W, X):\n",
    "    probability = sigmoid(X * W.T)\n",
    "    return [1 if x >= 0.5 else 0 for x in probability]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy = 89%\n"
     ]
    }
   ],
   "source": [
    "W_min = np.matrix(result[0])\n",
    "predictions = predict(W_min, X)\n",
    "correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y)]\n",
    "accuracy = (sum(map(int, correct)) % len(correct))\n",
    "print 'accuracy = {0}%'.format(accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# do it in a simple steps - Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression score: 0.910000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/barathiganeshhb/anaconda2/lib/python2.7/site-packages/sklearn/utils/validation.py:526: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "logistic = linear_model.LogisticRegression()\n",
    "print('LogisticRegression score: %f'\n",
    "      % logistic.fit(X, y).score(X, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.85831439,  0.05214733,  0.04531467]])"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logistic.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Support Vector Machines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sb\n",
    "from scipy.io import loadmat\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# getting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'X': array([[ 1.9643  ,  4.5957  ],\n",
       "        [ 2.2753  ,  3.8589  ],\n",
       "        [ 2.9781  ,  4.5651  ],\n",
       "        [ 2.932   ,  3.5519  ],\n",
       "        [ 3.5772  ,  2.856   ],\n",
       "        [ 4.015   ,  3.1937  ],\n",
       "        [ 3.3814  ,  3.4291  ],\n",
       "        [ 3.9113  ,  4.1761  ],\n",
       "        [ 2.7822  ,  4.0431  ],\n",
       "        [ 2.5518  ,  4.6162  ],\n",
       "        [ 3.3698  ,  3.9101  ],\n",
       "        [ 3.1048  ,  3.0709  ],\n",
       "        [ 1.9182  ,  4.0534  ],\n",
       "        [ 2.2638  ,  4.3706  ],\n",
       "        [ 2.6555  ,  3.5008  ],\n",
       "        [ 3.1855  ,  4.2888  ],\n",
       "        [ 3.6579  ,  3.8692  ],\n",
       "        [ 3.9113  ,  3.4291  ],\n",
       "        [ 3.6002  ,  3.1221  ],\n",
       "        [ 3.0357  ,  3.3165  ],\n",
       "        [ 1.5841  ,  3.3575  ],\n",
       "        [ 2.0103  ,  3.2039  ],\n",
       "        [ 1.9527  ,  2.7843  ],\n",
       "        [ 2.2753  ,  2.7127  ],\n",
       "        [ 2.3099  ,  2.9584  ],\n",
       "        [ 2.8283  ,  2.6309  ],\n",
       "        [ 3.0473  ,  2.2931  ],\n",
       "        [ 2.4827  ,  2.0373  ],\n",
       "        [ 2.5057  ,  2.3853  ],\n",
       "        [ 1.8721  ,  2.0577  ],\n",
       "        [ 2.0103  ,  2.3546  ],\n",
       "        [ 1.2269  ,  2.3239  ],\n",
       "        [ 1.8951  ,  2.9174  ],\n",
       "        [ 1.561   ,  3.0709  ],\n",
       "        [ 1.5495  ,  2.6923  ],\n",
       "        [ 1.6878  ,  2.4057  ],\n",
       "        [ 1.4919  ,  2.0271  ],\n",
       "        [ 0.962   ,  2.682   ],\n",
       "        [ 1.1693  ,  2.9276  ],\n",
       "        [ 0.8122  ,  2.9992  ],\n",
       "        [ 0.9735  ,  3.3881  ],\n",
       "        [ 1.25    ,  3.1937  ],\n",
       "        [ 1.3191  ,  3.5109  ],\n",
       "        [ 2.2292  ,  2.201   ],\n",
       "        [ 2.4482  ,  2.6411  ],\n",
       "        [ 2.7938  ,  1.9656  ],\n",
       "        [ 2.091   ,  1.6177  ],\n",
       "        [ 2.5403  ,  2.8867  ],\n",
       "        [ 0.9044  ,  3.0198  ],\n",
       "        [ 0.76615 ,  2.5899  ],\n",
       "        [ 0.086405,  4.1045  ]]),\n",
       " '__globals__': [],\n",
       " '__header__': 'MATLAB 5.0 MAT-file, Platform: GLNXA64, Created on: Sun Nov 13 14:28:43 2011',\n",
       " '__version__': '1.0',\n",
       " 'y': array([[1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [1],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [1]], dtype=uint8)}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data = loadmat('data/svm_1.mat')\n",
    "raw_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "visualize it as a scatter plot where the class label is denoted by a symbol (+ for positive, o for negative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fedace15d90>"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qqtTU1KTW1lYdOHBAO3bs0Lp16/qeq6urS+PHj9e0adN06NAhfeMb31Aqleo7Pn36dL34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\nGAAAAIFFGAYAAEBgEYYBAAAQWP8fTNvWsdgGOqwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedae0abc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = pd.DataFrame(raw_data['X'], columns=['X1', 'X2'])\n",
    "data['y'] = raw_data['y']\n",
    "\n",
    "positive = data[data['y'].isin([1])]\n",
    "negative = data[data['y'].isin([0])]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.scatter(positive['X1'], positive['X2'], s=50, marker='x', label='Positive')\n",
    "ax.scatter(negative['X1'], negative['X2'], s=50, marker='o', label='Negative')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearSVC(C=1, class_weight=None, dual=True, fit_intercept=True,\n",
       "     intercept_scaling=1, loss='hinge', max_iter=1000, multi_class='ovr',\n",
       "     penalty='l2', random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import svm\n",
    "svc = svm.LinearSVC(C=1, loss='hinge', max_iter=1000)\n",
    "svc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98039215686274506"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svc.fit(data[['X1', 'X2']], data['y'])\n",
    "svc.score(data[['X1', 'X2']], data['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with a larger value of C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svc2 = svm.LinearSVC(C=100, loss='hinge', max_iter=1000)\n",
    "svc2.fit(data[['X1', 'X2']], data['y'])\n",
    "svc2.score(data[['X1', 'X2']], data['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we got a perfect classification of the training data, however by increasing the value of C we've created a decision boundary that is no longer a natural fit for the data. We can visualize this by looking at the confidence level for each class prediction, which is a function of the point's distance from the hyperplane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fedacd9bd10>"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LxbCIiIiIhCwVwyIiIiISslQMi4iIiEjIUjEsIiIiIiFLxbCIiMjv5Pf78fv9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\n5ZZlWJIkSbllGZYkSVJu/X8fmGCncfmrDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedace9d590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['SVM 1 Confidence'] = svc.decision_function(data[['X1', 'X2']])\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.scatter(data['X1'], data['X2'], s=50, c=data['SVM 1 Confidence'], cmap='seismic')\n",
    "ax.set_title('SVM (C=1) Decision Confidence')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fedacce3090>"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p0oQFsbFUqFDB6YhSDmjOsIiInLXvvvuOAb17M6pyZa4LDWX38eO8np5O05gY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\n/wdC+QkChM2CeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedacd84d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['SVM 2 Confidence'] = svc2.decision_function(data[['X1', 'X2']])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.scatter(data['X1'], data['X2'], s=50, c=data['SVM 2 Confidence'], cmap='seismic')\n",
    "ax.set_title('SVM (C=100) Decision Confidence')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "The difference is a bit subtle but look at the color of the points near the boundary. If you're following along in the exercise text, there's a drawing where the decision boundary is shown as a line on the plot which helps make the difference a bit clearer.\n",
    "\n",
    "Now we're going to move from a linear SVM to one that's capable of non-linear classification using kernels. We're first tasked with implementing a gaussian kernel function. Although scikit-learn has a gaussian kernel built in, for transparency we'll implement one from scratch.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# examine another data set, this time with a non-linear decision boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fedacbe8410>"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Lly/HT3/607LoHXauuOIK3Hvvvdi7dy/WrVs3t339+vX47Gc/i4MHDwIAXnrpJezfvx8v\nvfRSoOsOCgUyIYQQQohETjvtNPz850/ggQeG8MADQ/j5z5+Ysx7bWbFiBd773veipaWlaHtdXR0m\nJx/CwMD/wIknbsV73/sl3HPPLvzpn37EVz5KxfSnPvUpvPzyyzAMA4sWLcI///M/Y2RkBCtWrMCK\nFStwww034NVXXwUADA8P47e//S2OO+44ZLNZrFu3Do2NpsvHeeedh/POOw8nnngi3va2t6GpqanI\nBWPt2rUQQmDp0qU4/fTTHfPS3d2NhQsX4he/+AUuuOCCue3vec978PnPfx6bNm3CkiVLcOKJJ+LL\nX/6yr+uWgVFN3Us/mWGIKM9HCCGEEKISwzCqWkrTwg033IBnnnkGX/ziF+POShmVnkFheyCTOy3I\nhBBCCCGkiMOHD8/FHz548CDuuusuXHrppTHnKjo4SY8QQgghhBTx4osv4oorrsAvfvELLF++HNdf\nfz3e//73x52tyKCLBSGEEEJIQGrFxUJn6GJBCCGEEEKIYiiQCSGEEEIIsUGBTAghhBBCiA1O0iOE\nEEIICUhHR0fgxTuIHDo6OqSnyUl6hBBCCCEkdXCSHiGEEEIIIZKgQCaEEEIIIcSGq0A2DOMuwzCe\nMQzjB1X2ud0wjP80DOP7hmGULzZOCCGEEEJIQvBiQf4igPMq/WgYxgUAThBC/A8AGwF8VlLeCCGE\nEEIIiRxXgSyE+BcAv6myyx8B2FPY9wCAFsMwlsvJHiGEEEIIIdEiwwf5LQBmbN9/XthGCCGEEEJI\n4og8DvL27dvn/u/r60NfX1/UWSCEEEIIISljfHwc4+PjUtLyFAfZMIwOAP8khDjV4bfPAhgTQtxb\n+P44gF4hxDMO+zIOMiGEEEIIUU4UcZCNwseJ+wB8uJCRMwH81kkcE0IIIYQQkgRcXSwMw9gLoA/A\nUsMw8gAGARwDQAghPieE2G8YxoWGYTwB4CUAH1GZYUIIIYQQQlTCpaYJIdqTzwPT00BPz/y2yUmg\nowNYuTK+fBFCCNEXLjVNCEk109PApZcC1tyL8XHz+/R0nLkiaSOfNztediYnze2EkNqCApkQoj09\nPcDoKLB2LbB9u/l3dLTYokxIWNgRI4RYUCATQhJBXx9w9dXAjTeafxkhksjGrSNGCzMhtQMFMiEk\nEYyPA3feCQwOmn8lhbokpIhqHTFamAmpHThJjxCiPZOTphAZHTUFy/i4ad3bt49uFkQuVtm6+mqz\nI2aVOa+/E0L0IcwkPQpkQoj2MIoFiQKvHbHt200L8+Cg+T8hRE8okAkhhJCQeOmI0YJMSHKgQCaE\nEI2gxTud0NWHkGTBOMiEEOITlREJOJkrnXR0mGLYshj39ZnfOzrizBUhRAUUyISQmkSliGXc5vhQ\n2fFZubL8Gfb0cFSAkDRCgUwISQSyhY9qEcu4zfFA6z0hRAYUyISQRKBC+DiJWFlCnHGb44HWe0KI\nDCiQCSGJQIXwufdeYNeuYhF7333AJZeEE+KTk/P52759Pt+lwpuogdZ7QkhYGMWCEJIoZMWgnZwE\n3v9+QAjgG98wt11yifn3ppuAm28OHspLpygWOuUlKhiKjRACMIoFIURj/LosVNtfpttCRwfwT/9k\niuO1a+fT2r0buOaacBZInSZz1ZpPLq33hBAZUCATQpRiF2j5PHD77cUCrVQsVxJ0990nV/hYItY+\nHJ/LAR/6kLsQdxLxX/ua+bEjK3pCUKxz211TLrkEuOMO+T65KqNH+CGKUGy6XCshRCFCiMg+5ukI\nIbXG2JgQy5YJ0d8vhGEIsXNn8faJCef9BwfNv2NjQkxPl+83MWFul5E361xDQ/PnrJTHiYnyfVpa\nzE+148IQ5Prt+RwcFAIQYsECeXmqdC4h5F+/TtTStRKSZAq6M5hmDXpgoJNRIBOSGGQLUkugZbPl\n4rfa/oODwc7nBSeh09oqxPBw+X6l1+0k4p22qcyrF1E2NiZEc7MQTU2mOLaL+LCUlhGro5DLyb/+\noPgtx173V/msCSFyoEAmhEhHppWsVExks9XFb1TiI2wnwEnEqxT2Qe7LxIQpjq08ybR2OpWRBQvU\nd2z84Lcc+9k/ik4cISQ4FMiEECXIEKqlgmPnTtPNor/fOc2kDF9HbUG28CvKRkZMq649TzJcUyzs\n19zcXH4ur6hyoSnNo5d8edmfFmRC9IcCmZAaR6W4CGsls+fNEr9DQ+Z2J/Gr8lpk4dcHWdY1+RVl\nUXU2rDLS1BT8XLLyWule53L+ynG1ci8jr0HKRBLeDUJ0ggKZkBpHlRCSbSVLSwPvdB2jo+bHjl0c\nh30+QdKI4n5b+cjlyv2b/Z5LxYiF5YPtx7Ltlg8Z9zXI80zK6AohukCBTAiRLmbZGMsl7POJu3Ph\ndP7hYXNSo8wyIsOv136v/UYXibLcBykTdO0gxDsUyIQQIYTcSUNxC7I04vX56HjvnYTjkiXeIn54\nRab4s+51LqcmioUsgryznBxIiDcokAmpYawGvdRqNjISd86iRUdRaceP+NPVeq9jGDsnkmJlpQWZ\nELVQIBNSw0xMFA8j230u4xZUUaKrqBQiWN50FUJerZePPFJuXR4eNrc7IauDU+lej47q1YGiDzIh\n6qFAJqTGUR3Kyw1drLdBRaXq/AdNX7ehdD/3d3i4eNVEK7xfqWiWTaV7PToqT1zKKC+MYkGIeiiQ\nCSGxiimdLFtB7oNO+bdwEqNxCqQg98gSxb29xWI5LmRZ5WWXFwpfQtRAgUxIjeOn4VfVGMftEjA9\nbcZXtufBirfshbjzb6eSABsejk/IBy03vb1mS9Pbqypn/nDqQAW5NpnlRccOGiFpgAKZkBrGr89l\ntaFmFUsvV0OmWJcxpG/lv7+/OH/2PEVh2at2XyoJMx2tkF4syFHmu9K9CypQZY7a6NRBIyQtUCAT\nUsME8bmULRTs+/pp4GVazmRZkPv758WcNQGyubn4vsVt2XMSZrpZIb12WKLKt9t5/JZfFYJWN59z\nQpIOBTIhxJFqjXilxjhqoStLaFgdBft1ebVElubfEnP9/f5XYfOb39J8uOW32v3SyQrpJ4pFFPn2\ncr+9ClQVol6nZ0dIWqBAJoRUxKnRd2uMw7hKBHFLkGE5s1t7Bwf9hbpzEk/9/fN5UmHZUxXmq1pe\ndXTDsIjbehqnH79u1n9C0gIFMiEaE6cocWr0ZQ81l1KavhWCzn4P7NcvM7KA3dprd43wiz1PqizI\npefxkrZTWRodNT/29Pr7zVXuStPzK8SiKrtxW0/jFqiV7vMjj+jboSEkCVAgE6IxUTa+9obWOq/l\nh+tlwQRZeR0bE6K11RRq9kVMJiZMwWylKdsHOaiLhR17nqLwQQ5rObU/52XLTPcQ+/fSvPoRo1GU\n3bjFqRD6WtZ1uDeEJBkKZEI0JyoLmb1BtU9as4vmqBYisFwUslkzP83NQjQ1zYtlr+fzkyfZFtlS\nd5HpadOP1n5u+29xhQqzd0hKJ106nd+PKFddduMSp1GeN8y54rauE5JkKJAJSQB2UaKycdahQbXy\nkM2ak92yWVMcB7GUerWiqfLp9bq/zLSC4FX0upUPN3/sqFH1rkRpnQ17rrj9swlJKhTIhGhOqSix\nLLuqGmfVDWo10VIqBrJZMy+NjcFFuxfRryIqhN/945ro5fW8XoRatYgeafMPjqozGSYEYRwdXl1d\nTgjxCwUyIRpTqYEvbTBlNXxRNKjVRIu9cR0bM10qGhuFWLzY/B5U4KgU/X7TrrZ/1NY+PwLSq0uL\nVTatmNCbNhX7sUc9qU9lmY7ieVnPyOosZrPe3oG4fJDp+0zSAgUyIRpTTTTIbpyjbNjcRIuVl5GR\n8glufkWTSoEUlwVZFqpCjlli7rzzvPuxyyp/qt08rPTtz6ulxSyrKpieNjsZ9lUFrU6Hl3zaicqS\nq4OrFiFhoUAmkcLhNzmoaICifjZRxNxVKfrj9EH2inUfSyOU2LfLxssS0ZWQUa5Vu3nYo5NYoxpW\ntBUVnUlrVcHzzpvvdFRbBl2XOpa+zyTpUCCTSIl7+E2XxiMMcd9DGUTpv6nqeftNu9r+qieTeQ3j\nFpag7gB2ZAgrq3zZl/62bw973VZ87tIY4aqiWPixIMuoH8KWR1qQSRqgQCaRU63yVC1g0yAuky7y\n0/AMvCLrWckI9WWPCuJHtPg5d5gJZfa8yhBWltC+4ILi7ZWWrA6avmoLqVunw+n5DA2Zi73IWrDH\nzztaS+83STcUyCQWKjUuUVSutG7ES1QCX4eOhKzyHDYd633r7fUv6vyce2LCjKk8NFS8b2n857Dn\ncUO1BTnKOsSt01HpvoX1uw56jTq8d4TIgAKZRI5bxRtF40P/uPSjiyVLVnkOms7YmGlNtHxXLQuk\nCsuutRiKfR/Lmul231X5navwQZYZ+UPG+Uqfj+VKE7bMsZ4ktQwFMokUr42LyoqZFuTaQdazDit0\nZJVnv+lY79s115gi8eqrze+WT2uliV5hzx3nOxZVFAs7lcpClP7A1vMp7QgE7RiyniS1DgUyiRQv\nlb3KilkXqyKJDhniNEy5idOCbI9WYY9PbLlBqPQN1sX6GLfQi+L89nPYXVwsVFitCUk7ygUygPMB\nPA7gxwA+5vD7mwDsA/AYgCkAp1RIR/nNIPGjumKmf5x/knzPZIoTK61czoxgYE9LpQVRZjpBRGuQ\nc8ctSi10EXoqOwsqrjHJ7zwhslAqkAHUAXgCQAeADIDvAzipZJ8dAD5Z+H8VgP9TIS31d4PEDivm\n4Djdu9FR82OnVqxJKvJtCZ0FC4L7oI6OCvG3f1u8fWLC3B4kRJzXfYKK1kceKXfFqBYJQqfyokN9\norqzUHqNlh+4/RpZhxLiH9UC+UwAD9q+31BqRQZwP4Dfs31/AsCxDmmpvheEJBonYWItYKCTP2IU\nomV62hScfkSoG/Z7YC0UEeR+TEyoWWiimjCNMmyXDqJUF+LoLOjUQSEkyagWyGsAfM72/UoAt5fs\n878B3Fr4vxvAawDe5ZCW8ptB4kOnBR2SjJOQlSVuZQ0TR9GAyz6HU3pNTcHvhyWKFyww07HEclgq\nPWsu/BAPcdU9UT2vWqpbSe2hg0BeDOALAL4L4MsADgA41SEtMTg4OPcZYw2dKmQKmtJK27LYjYyE\nTzsJOAnZsOI2iP+tl/Simrgk2+ptCdxcLnja1jOR7Zuqyt9Vl0l3pVCkORPF86K1mqSJsbGxIp0Z\nhYvFQ7bvZS4WDsf8BMAih+1q7wyJHVmCxqnSbm4uXxo2jaiwINvvp909YGIiXIMYRQOu4hwyREHU\nFuQwhF0dTzVJE2lRCPooLf4cXSBpRbVArrdN0jumMEnv5JJ9WgBkCv+vB/ClCmmpvxskdmQJGqdK\nW7UgU9HwhY25GsQH2W3SjwzradIsyHbCPuc4fJDDMDxcvBqdtfCGnxjKqvH7rOO0OqsW9HF0GHQd\nXSAkDFGFeTsM4D8B3FDYthHABjFvZT4M4EcAvgagpUI6EdwOEieyBY290paVdrWGVUXD5CdNWVEs\nvJwzTIOYRB9kmaiYQGilq0L06W5BtvBTJuMuH159xYNEpLDHvrbSsn+X/dxoQSZphQuFEC2Q3WCV\nRhyQEcnBSz5VNBZxNEDVzhk2P1FFsVAlFmvV39UuQHW7D0HKpMr3ysv9cRL0pfXL0JBprbcW/lAZ\nfSQIcXc0CFEJBTLRAhlxXu3b7JX2yEj58HWYxtzesDqtWiVzWVuLOIYwvTTgtdYg1ur1l4pJy6Ks\nw30I80xUvVdhOtKlv+3cGVzIy+4EMOYyqSUokEnsBBW+lRrCKKxbVsPa31+cJ8s/84ILirf7Pb/9\nGqzrtJYIjtOCrJvlMA6SOqQc9NlVeu9K3S7iug9Br0v1c6yUfhAXpjBCXmYnoFY7iKQ2oUAmsWNV\nuiMj5ZERShs6HcRJJQtPf78pjjdtKt5uCQk/jYh1T6xjw6TlFzaC7iRxUlLQ51pNgCbxPgghv4xX\nuke5XPn98bvioU4WZFVpEqIjFMhEC6yZ/AsWzPsLV2q04myUKzWslltFf3/5dq9WX6dYu4sXC7F2\nbThrtF9oJa5OkgWCzLwn+T7ILuPVIsj4uT9J8UFOaseIED9QIBNtsCrdBQucG5UoZtO7NZxOvw8N\nCbFkSXnOnPnQAAAgAElEQVSe/TYiTg3aggVsiHQiDdZ1GeImSfchqg5f6cRge2zroNb6MD6+qq7b\nuhZZiwYRoisUyEQL7I1LpSV8o4jH6rfhl+2fab8PtbK4ic6kbVKSLKtvkkYZohTzVucjl0vO/fGD\n/V5OTMzXUaWucYSkAQpkEjv2SndszKx0m5rKrRNRxWP1IyKchMLwcLFbhd+Gw2pkm5rCN+pJEjI6\nooOlVNYz1OFa4iIKdxDV57CXA+t/ezmI4r1WseQ6IbpCgUxix17Z260TIyPx+SCHOUcYQSN7+LKW\nRZEs4va1lfUMa72zpLLeiOI9K60fZS35Hhb6I5O0QoFMtOGRR8rdJYaHze1C6GlBlomqRjZugZcG\n4hYBtfQM8/m82LRpQJxxxjli06YBkc/nQ6cZpXXXQrWfcxAXLNn5rKVySWoPCmSiDW4CUUcfZJmo\nbGTjFnhJRhcRkKZnWEkE5/N50dq6QmQy1wngQZHJXCdaW1d4EsmV0kzbKIq9HMiYCBz0XqTtvhJS\nCgUy0YpqYkSHKBZJRBeBl0R0EQFpeobVRPCmTQOF7WLuk8lcJzZtGgicZpreaRmTeGtxoiYhQaBA\nJtrhZhWJyz9YB/zmXxeBl1R0KC9pe4bVRPAZZ5wjgAeLfgMeFN3d5wROMy3I9EF2q0N1KPeExE0Y\ngVwHQiQzPg7ceScwOGj+HR/397sb09PApZfOHzc+bn6fng6bc2fyeWBysnjb5KS5PQh+89/RAezb\nB/T1md/7+szvHR3Bzq8bMzMz2Lx5K7q7z8XmzVsxMzMjNf2VK4GenuJtPT3mdplUKyelz/DtbzfL\nv/0ZOpUp2WVPFgcOHMLs7NlF22Znz8bBg4ewenUnMpmHi37LZB5Gd3dn4DTTgr0cdHQA//RPwP33\nm//7ea+91KF+6hldyxkhsRJUWQf5gBbk1ONmKZNlSfM6xBhk0ZBSK4sK65+s/MtGxeQqt/MF9VfV\nDT/lxOu+ulqeq1l7gz7TJFiQdbDK+ikTXusZXcsZIWEBXSyILvgVpGEWbfDipiFLsKtYecqe/0r3\nbXQ0uoYrDrGaBFHkBz++oV731dF32a2sWB2t7m7vHa0kdJZ0EJJ+RbpXdzYdyxkhYaFAJomltMEZ\nGZlf1cm+T2nlL1OIeE1L5uIfY2PmQiT9/fMTFe0TFu3pymq43KzDcYjVoP6qOuPHv97rvjpGvwgi\nguNIUzZJEpJ+86pjOSMkDBTIJNHYK3Fr0ko1ARrEihN20qCMmeel+bdE8c6d5t9Nm8yQd5Zotqcb\ntuHyYp2LQ6zqZEGWMXwuo+PGlc684cUdSJXLUBKEpN96MknCnxCvUCCTxGNvcNwqar9CJqwF2amh\nWbAgeANpz7917v5+IZYsESKbLU9XRsPlRYi67aNCbOg0rG5/zvZwhHZ3nGpiWZYPcmmkA6tDFvdq\nazrhpdyoKltxCMkgnTc/x+jgOkKICiiQSaJxanBkWWhk+CCrtuhZ15rNlt8HWQ2XF+twNUGhUsjq\nNKxu77DYF7Txct/9CBK3fVX4vKcJGR2+IMQlJK3zjoyUd5RklAcdJh8SogIKZJJYnBqclpZwLgx2\nZESxcMtvmAbSTZCNjsppuLyKhUpiVQdXiKgibFTrsESJl0mctSpgvHT4VLgMxfkcrLqxqWneDY2W\nXkKqQ4FMEktpg2MFzx8ZMb/r1gB4aSC9NqJhh/T9ENYCHPdkuqhcMUpHM5xcXqKgNB9W2eAQuElc\nFuQgyBTV9onCKjpuYfLKThzREQpkkhqirmRVnM+rlTmuGMdBXBniFhtRnL/0ue3cWXnSpBeCPt9K\n5ad0ifZankQVpw+yX2SNOtk7TWHmQFQjTF7px0x0hAKZkAq4iRRVlXraZoTHLTaisGDby4o90khp\n2D2vBC1b1cpsEqInRIWXDp8u/u1h6wN7WbJcLRYsKPdPr4SfzlqQvFrpl0YkskYCCYkLCmRCKuBF\npHgNt2Wl59XCmzYxE6fYiNqCLcu6L7OjlOROl2r/8ahXgAxCmPrAKo+lEU5GRrx1uvx21vzm1Z6+\ndeyCBbQek/ihQCakCl6EhVODEMa6nGQxoyNxW7DDIKOjFOfwdVjxqfrZxVk2vHakZNUHYTpuXvMQ\nNK9jY+bkwaYmf9ZtQlRCgUyIC9VESrUGIUhjUUu+eKXiaWpqSpklT5fhcj/IGp2IawKUDPGp2vof\np3+8l3ddp/rArbMW1ge5qWk+/TTXeyQ5UCCT1CIjakQ1keulQfBrAayV2dyl4qmhYaswjIWioWFD\n4qy8KqhWtnQSTdWQsXiMDP/xfD4vstn1oq1tlWhrO0Fks+vnzhV3hBW3TvQjjwgxPFy8bXjY3B4l\nXjr7YRYkGRmZD89p+R+nsd4jyYICmaSWsBYat+PDiOtax0k8ATkBDMQaVksX0lC2qolPr9blsBbe\nfD4vWlreLIBrC3kZEECraGlZPifQo14BspRqnWgdOkMTE+ZKnUNDxXkYHg4vYK3QnPbYzFYse5nX\nWCuGByIXCmSSarwICRUT7XRo2HSmkngCzonFkpdEdJ/IWU18+ll8JoybxqZNA6KubktJObtOGMbq\nOcEbxwqQFmHqpyAEtfIODxefe2hIiNZWOfWZ3Xpsn0QoU7yyPiZBoEAmqceLkJAtNuwNkX0WuT1E\nXJzWC9mWMb/pybQgJyEKgWySYEGuJjD9uDaE8R+v3BE7Y+5cca0A6Ue0yaqfdJ08HEVnLwnvDNEL\nCmSSarxUiqotGLpZL2RbxoKkV35MMB/kJEeocMKLhU+38lSNuJcfd7MgV0O1f3LUUSxkpJfLlQvZ\nsHVllMJV91EXohcUyCS1ePVBjsIHTifrhQy/TrvFNptdHyi9UvFkRbHwYymMe5U+2Xgps2nwp4yq\nY+Pmg1wNHcqWqs5QEKFo1Y1NTcX1ZZj8RNnZ06kOJsmAApmkFj9RLKJYxUkX60UYy5iTsKmvbxbA\nHmWWNn/XkhfAGrFwYXti3S1qpSGPKvRetSgWbsfFPTqhojMUNvykJZRlxCuOqrOXpFEXog8UyERb\noraUqRSwOomeMJYxp2Pr6nLCMFbHYmkrzk9eACsEsCXx7ha6dKZqnSTGz65GUKFYWhdb5TOXU5RR\nyTi1JaOj5sdO0kZiiFookIm2pGX4TTfrRRjLWCXrc339slgsbcXXsqYgjqMX6jLRqTOlO7U4QTMM\nMowOaSmfutXLRD8okInWqAjBVorqilJHn9GglrFK1udsdn1slrapqSnR2dkt6uqODeU6ooPQYqPt\nHR1cIGqNtJXPsGKflul0Q4FMtMPLcJ7MilpHAasrUYsSN+Eqw4Ksk9BiWfSODpPovKJLBywsuqzs\nJ5Mw7kxO7VBLixCLF6tZWIVECwUy0Y7SCSHNzebM6dIJIUkb6kuL+IlycpWbcJXhgxy10EpLOYib\nuJeJtvDXiZPTAYurDOluQfZ7X2S0IU5pDA0JYRhCZLPmtp079bpPxBsUyERLnGZKO1XGSZrMpHvj\nohtehKuMKBZRCy0Z5SCMQIpaXKmynvrp2KjKg/9OnJwOWJx1ic6GCT/3ReY9dGqHsllzW2+vfveJ\neIMCmWiLW1B6rxW1LEFQqxNc4hoe9iJcZYiPOIbqw5aDMI17lOJKpvW0tBxOTU3Z0t4jDGO1qK9f\nVhbGTaULTbBOnJwOWJAyJKsu1NkwEXW74HQ+a1tvr3mfsll/aRI9oEAmWuJWyam2FDhVnsPDQixZ\nEl5YqGhc4rSQqcKL+JCRv7iuMWw58COQSsuzNUKTy6ntqIXpfNjLdDa7XrS0LC97RlNTUyKbXS/q\n65sLK+aVPz+VHaCoOnGV8FuGZHSOktDJj0rAV/JBbmmZd6vIZk13C8snmSQHCmSiHSpWE/NbqVfK\nw9BQOOvEyIj8xiVuC5kqvF6XDJ/oqOPdyhIZXoWAU3lesEC9iAhqPS199qb4bS240BSXQ7cyqtKF\nJqpOnBNBy1CYspcEN7EoBXylKBY33VR87qEh07ii030i7lAgE+1Q5SPp16pQqaL1kk41y4LsxiVu\nC5kd2ZbstC3UIIQ8keFXCNj3b242y6JqERG0bDodZy4TPVBWDt3KqMr3I8pOnJ2wZSiohVX3Caa6\nCHjd7xPxBgUyqQmCWhVKGxI/6ZTuOzKiptKM20JmEcRSlpbwV36Q0XgGFQJWeW5q0tsHuVKZBs7x\nbUFW7UITRycuTBlKgotEUChMiUwokEnqCSomShsSy73CTzpR+MIFsZB5FaZ+xIXffOgUf1gH/DTu\nQYSAVV5zufKQiVFEsfAjIJ0tyNcUljQvLiteylEaRyKCQAsrId6hQCapJ0hl7NSQtLaWB8lXHWPT\nC36FZpD9vYiLapZsJ0GepIUeokCleIk6ckXYUQGnMtrS8maRza53LIdeyqiffKV1ZEMXYaqLUCek\nGhTIhDgQtiGJugHwYyFTJUyrLUPtJMi7unqVuYYkFVWdqqiEkYqwbjKsvn7yFbQDmTYxrRqdXD10\n6TgQvVAukAGcD+BxAD8G8DGH35sB3Afg+wAOAeivkI7ym0GSg+4Vms75U+WzXCosGho2iMbGVrF0\n6fGFKATFwrmzs5sWZAd0jjHrhq6jAn7ypdrvnsyjS1mXbdDQuf4n3gkjkOvggmEYdQDuAHAegHcC\nuMIwjJNKdrsawL8LIU4DcBaAWw3DaHBLm9Q209PApZcC4+Pm9/Fx8/v0dJy5mmflSqCnp3hbT4+5\nPW5Wr+5EJvNw0bZM5mF0d3cCAGZmZrB581Z0d5+L/v4N6O/fgO7uc7F581bMzMxUTLe9vR2PPTaF\njRuPoqvrM6ivH8Ubb/wv/PrXbTh69NyifWdnz0ZdXSMWLdqLTOZ6AA8hk7keixbtxbZtOddrsOfR\nLV9+9lVxvB/Gx4E77wQGB82/VvlOCgcOHMLs7NlF22Znz8bBg4diypGJn3z52XfHjl04cmQdZmdv\nAXA+ZmdvwZEj67Bjxy6p+VdFPg9MThZvm5w0t3v5PQxByrqq/PT0AKOjwNq1wPbt5t/R0fI63Cu6\nt08kAtwUNIAzATxo+34DSqzIhW13FP5/G4AfV0hLcV+BJA2dhuh0QMbEu+Lf9ggz9uy1vq1jxVa4\nAQE4W+SCDKOrHC6Xfbwf0uCXuWnTgGho2FB45ucIwPyeVgty1MuUy8atzKkqk0HTVf2OyLRos31K\nPlDpYgFgDYDP2b5fCeD2kn0WAfg2gKcBvADgggppKb8ZJHnoMkQXN7Im3nkVtm4UC4e8AFYU0gsv\nMlWJnbDnCovfYVkdh3GnpqaEYSwUwJbC898iDGOhmJqaEkLE569bvvBITtTXN5ctS+20r8zILTri\nJuRUCD0dw9SpSJftU7LRQSCvAXBr4f8TADwFYJFDWmJwcHDuM8buWM3DHvo8shrqYmEb3DpWnp+8\nMIzVoq1tVWhh5MdqF9bCp7OFUEeLs2lB3lpSDrfOPfM4/XXz+XxhWeplhXBxe0Iv7BH3NcnCTcjp\nJvRk50fFu8T2KXmMjY0V6UzVAvlMAA/Zvju5WNwP4Pds3x8GcLpDWqrvDUkQnFRRTCUh19XV6ysd\nWRZkXZa/TpIFOQi6NcLVOhQ63EsVeUjaQiGlVCtD09Pz8d/t8eDjrBd1s2g7oWPnlfhHtUCuB/AE\ngA4Ax8CMVHFyyT53Ahgs/L8cwAyAJQ5pqb8bJDHIrtBGR8uXgW5pMbcnASfLHZATjY2tvhpsWT7I\nVloqhENafZCDopN1r5oA1cEar0MeZCBLgJWmMzJi1ntWOsPDQhiGEJ/8pPl9507ze2k8+KhIivBM\nusGFmCgVyGb6OB/AYQD/CeCGwraNADYU/j8OwDcB/KDwuaJCOhHcDlKrTEyYDUNzsyk0mpuLGwrd\nyefzorGxVcz7fl4ngBWBJkjZhW02u77i4gxx4kd8hxXqTsfrEvtWNwtytQ5FWi3IcSHj2ZcKOase\nHBkxv4+MCLFwoblNpgU5qICk8CRRolwgy/pQIBPVjI0J0dRkluymJrViQ0VFf+qpPQJYI6zoAebk\nuORZx3QnTquyvdxY1jRLsOhiTavUIdHBGq9DHmSiYvTASXgnweeXENlQIBNSYGxMiAULzJK9YIFa\ngayigUiTdUxn4rzP9nJj9w+1i2adrWmyrPlhl7GO2mdYBSpHD+yCWJXPr26+zYSUQoFMiDCFheVW\nMTg4727hRbAGtQbLbnjito7p4nagmrj9WHVzq4iKKJeA1r0sq7TA2stXS0v53AyZcZCzWfP9yWZp\nQSb6QYFMiAg3SS9MYyV76DIuC13c4jxKdLDU6zQxLyqiWgI6CWVZlS+u26Q9WecRYn7CX2+v+Xfn\nzvBpEiITCmRCRPgGJ4hVTzdLYBhhoDJ8lm5WvLgFlG7lJir8WO7DlEcdOkBxIVN4V0uLFmSSBCiQ\nCZGEH6uejpNU5oVBXlhLBRvGapHNrnc9VrbbQdwi1I24/Fh1LDdREdUS0HG70KSFamWVPsgkCYQR\nyHUghAAAxseB228H+vuBO+80vwPA5CSQz5fv39EB7NsH9PWZ3/v6zO8dHZFk15EDBw5hdvZUmOv7\n1AEYgBC/h6985V7MzMxUPXb16k5kMg8XbctkHkZ3d2egvOzYsQtHjqzD7OwtAM7H7OwtOHJkHXbs\n2OUrnZmZGWzevBXd3edi8+atrtfhlfb2dgwP34oDB76F4eFb0d7eLiVdN3QsN6XIvOf2tF588UU0\nNf09MpnrATyETOZ6LFq0F9u25cqOC1MevR6rqmylhZ4eYHQUWLsW2L7d/Ds6am6fngZuvtn8vn27\n+ffmm83tgFlnTk4Wp1epLk0Cabse4oGgyjrIB7QgExtuQ4Gyhgq9pGMPt7VsmelLZ/8e1roXlavB\npk0DhSV4i610dXU51+FlrxZfr9ciw4qnuxU6jci8505ptbS82VNcbtU+yCxb3nEaWXOrV5MwUuKn\njUnC9ZByQBcLkkTcKhxVK005pWOvKK3f+/uFWLIkWZEp8vm8qK9fFliYurkd+LkWGX6gafQlfeSR\n8lXMhofN7VFSqaMj856HTSuMG4zbsWksWyoI4y8f1tde9aIiftuYWp07kGQokElicatwZFVIftOR\nGWEg6oY4m10v6uq2KDlfVFEILNLoS2ot/WvN+I9j6d9qz0bmPZ9Pa94nHlgjurp6FFxV0Lylp2zJ\nRoaRIkxdGoXVNs62gaiHApkkGqvCyeWcrQW5nJwKyWvFJttKEHVDrNJi7fdawk6ES6uVL+7wWNXu\nq2wLckPDBgGsKLj9PCiALaKxsTV2V4a0li2ZxBEZSEUabsTVNhD1UCCTxOIW0N7aFpUFOS2r46mK\n0BD1tZSL/a2isbFVnHpqj1Zh44LQ22vev97e6M9draMj2we5sbFVAKUjGltjF6L0QVaLzLpUpdU2\nzraBqIcCmWhNJSvE6Gh5heO0El4UPshueQ3j86ZzQ+x38mDU15LP50U2u160tZ0gli17hzjmmJaC\nRVKv++gXnS3IQpR3sKampgJPMu3q6g09gqJqkut8+Vol2tpOENns+ljLk2qf2yiRdS0qrbZxtw1E\nPRTIRGsqVUKjo9VdKiq5XKiIYqGauGLuuuUpyLK/p57aIzo7u0VXV6/SaynNn+lX3VrwZ43GEh8W\np7J37bVm3nX1QQ6zrxMyJuqp6pTp1nn1Kth0qNOiQLXVtlbuYy1DgUxix62i8WoFoI9XOaqsZ1FP\nuPOC/Vo7O7sL1mK75XGg8AlmiVRN6XswMWGOhIyMmN/HxoR405tMkWwnzigWbp22uAWuSrceHf2Q\nvdSBtTLcTwFLwkKBTGLHqcJesqTYKmafjOc1DRmVfpIrWV0m3EUhJEqvFcgJ4Ngii7G5/RxtxEwp\nTmXY7jaUxE6frHjWQUdQVE5y1TWShRefWxoTCHGHAploQWmFbS2yMTY2P+FuwYLiiXh2VAnZJFtb\ndLGeRSEknPJjimS7xfiawkIo8Q+HV8JJuCQ5NFTcVlZd3oGo8CN8k1yuCIkCCmSiDaUVtiWMm5rm\nJ9zFIVCTam3xI0xVTriLQkhUulZg1Vz+vK7CFjf29yCpZc+i3Bc8J+rrmyOb0FaLPsgjI+b/9rqy\n1FiQ9HJFSBRQIBMtqFRhO8UxjsPFQaW1JW4/4aANvdeh7yiEhPO1bhWdnd3aC2I7bqELkzJ6YceK\n9lBfv6xgwd8jpQx4fW9UTnLVaQKtNYpmH/WamDAFs4pVRglJOxTIJHYqVdiWm0XcS416tbYEOZ8O\nFq6ofIQtIZHNrhfZ7HqpHQLdrHkWfspE6XswMmIK5NKJe0nwfy8laBmrJILjmPgZtwD2Q7U6K8nz\nKgiJEgpkEjtOFfbwsBCtreGsHDIsJX7SCHI+1eLUi4UryslGqjsEuljzLBgr1SRIGatWVuKY+KlL\np8sr9DEmJBwUyERLorD+ejlHtX2cfhsaMoW9V6t31OLUyRoW5WQjHSc2qYb+nsGee7Vj4pr4mZSy\n6qfMpbljRkgYKJBJ6rFbUuyNgWXdGxoyt/u1MFeyDvb3e7fcRNUIV7OGRWkp0zU0lmpq3ZoXpIxV\nKyuy3xunzqPXsqqbG4bfkSz6JBPiDAUySTXVwscJMb8SWX9/MOteafo7d/qzFkYlTv0uD6yqkU+y\nVS4oMn3Yk2zt81vGqpUVme9NpbSy2fWuZVVHN4wgZYSjHISUQ4FMUovXyX/ZbDjrnmUdLBXZXi0x\nUYjTMJZbmRYyHQWFSmT7sNeStc+trIR9b6zj29pOKCxFXiyEs9n1rmU1TR2+Wh/lIKQUCmSSWqpZ\nUqzGIJsNZjmx0rZbXhYvFmL7dufzxU2YKAJeBK0fEa3jZDpV+LXmebHk1ZK1T1VZKS7X3Y6dx7a2\nVWJqaqrq+dPiMlRLZYoQr1Agk0QTZjixv990r9i5s3i7F2vcxERxnFr7ssA6WvOCWm69CGsvaevm\np6kzXix5tPaFo7hcDwigdBXGawXQLlpaljuWVTfrc5IsyLU0KkGIHyiQSaKZmBBiyRLTbUKI+cp9\neNg91uz09Ly7hX3inleLrxWn1m510cVi7EQQa5wXC5kX/+YwC5GEEdVJE+a0IHsnzLPt6uq1leu8\nAFYIc2nyBwt/jxXABgG0imx2fdl558vzHgG0FgR1Ml2GkuzXTohKKJBJ4hkaMi3BlruENVEuiliz\nabfkebEgu4noIO4dMnyVk+bvXCs+yLI6PkGfbT6fF42NrQKwW37zAmgR5tLkA4XvpnW5re2EouPL\ny3NeGMZq0da2yrN7UVI6bITUMhTIJBVYE+16e6OzqtWCJc+LEHETwEH8NGVMfkraBKq0R7EQQl6n\nJcyz3bRpQDQ0bChYja+zWY2XVPRFthPU7zisqKewJiRawgjkOhCiAePjwAMPAL29wP/9v8D73gf0\n9ak95+QksHYtMDoKbN9u/l271tyeJtrb2/HYY1PYuPEourtvw8aNR/HYY1Nob2+f22fbthwWLdqL\nTOZ6AA8hk7keixbtxbZtOQDA6tWdaGj4OoCtAM4FsBUNDV9Hd3dnxfMeOHAIs7NnF22bnT0bBw8e\n8px3GWlEycqVQE9P8baeHnO7n310ZseOXThyZB1mZ28BcD5mZ2/BkSPrsGPHrrl9ZmZmsHnzVnR3\nn4vNm7diZmamLJ0wz/bAgUN4/fUPAJgCcBTAbQBm0Nq6EMBDJXs/iAsu+IOiLatXdyKTebhoWybz\ncNXyDHi7didmZmbQ1XUmdu+uw6OPDmD37jp0dZ3peF8IIXpAgUxixxKqf/EXwL//O5DNAnv2ALff\nrva8HR3Avn3zQryvz/ze0aH2vHHQ3t6O4eFbceDAtzA8fGuROLZ+ryair7zyg3jjjbsBCAADAATe\neONuXHnlByueM6gIkZ2GLuTz5Z2vyUlze5JwE7ZexWCYZzt/bDuAWwF8C5nM23DxxeejpeVe1NUN\nAHgIdXVb0NLyVdx88yeLjnfrEAa99koEFdaEkBgJanoO8gFdLIgD09PmhDy7i4O13HOS/DLdSPIQ\nqzmkvbVoSNowcmWTn+zUog9yNdLgeyyEu2uEV9eJsO4K1VaV3LRpQHR19YrOzm5x6qk9ju9bkAmv\nQd1C0hJKjpCkAfogk6Tj5pdJv03v51Ehwis18MBSkc2ur3geGTFw0xRzWQef97BlxK0s+xGDYZ7t\n1NSU6OzsFgsXtovOzm4xNTXlOY9BURlqkRAiHwpkknqSbn0LGgXCj5BRKcI3bRooixVrTopaI+rq\ntiTWqhsHcUZNkVVGqgnbKMSg23WofN+CiPo0jYQQkiQokElNoIP1LSh+h1i9LtFrb8xVCpN8Pi/q\n65uFGT7LihiwQlihtGgN80bcZVgH8SoD2VFXoshzmkZCCEkKYQQyJ+mRxNDXB1x9NXDjjeZf1VEu\nZOJ1QpI1+//008/Bb3/bjtnZa1A6qafSJKjJyf+nLOJDe3s7rrzyQzCMfwWwAcAMzAgC7VLPk2Z0\niJqiKiqIPWrFjh278OCD+6pGTal2fKWoF36u45RTjkdd3beKfq82ATCKSXRuE2UJIXrREHcGCLGT\nzwPT08VhsCYnzcgSTz0F3HknMDho/u3rS45I3rYth7vvPhNHjpgNeSbzcGHW/NTcPpbwNRvqXQD+\nGcCZsISoKQBuK2nMgdnZ83HkCHD06AQymYcxO3v+XJoyIz7cfPMncd99Z+K3v22HEB2wxLHs86QV\nK2qKVbbjiJqyenUnvv99uWWkuNwO4Pvffxh3332pqyiufvyZVY+vdh0zMzP4x3+8D0ePvgbAAHAO\ngAfR1PRVbNt20DE9U3APFG2z3jdCSI0S1PQc5AO6WBAXKvkal0a5SJoPshDuQ6xOw8bmIggDRUPI\nlYaPu7p6IhkmzmbXi/r65oJPMv0pk0QQ1x03nMvttaKzs1tZZIhq1zGfXr7w7pwjDGN11YgrnERH\nSDoBfZBJmnDy00x6FAsvVI4UcUYFAVDemFcT4TIjXNCfMrlUenZB/XArl9tVoY73sqqd03UESS/o\ntR3hrcUAACAASURBVCc5dCMhtQAFMkkdcc70jwsn4VtXlxNtbSeEFjKcRU/cCGpFrTbyEfT4MNbb\noOn57fTxnSJEfyiQSaqIe6Z/XPhpcP025roPIdMSFz9hLLmtrSsKkU0eLIhjK8JJ+fGlz3pqakqq\n0IxKuOr+ThFCwglkRrEgWqFipn9Slvh1W+65dF8/M+JVRS+QgdeliYlagi79bJXbzs5HAOQAHIU1\nsbT0eKdnfcEFl1aMeuE1ukW1KBrr1j2Piy9+H9as+RNPETK8ovM7RQiRQFBlHeQDWpCJCyp8jZO+\nyIgMstn1Ari2xDp4TdWJS1FBS5weBHXdsazB2ex60dLy5qrH+3nWXvPjtuy0ysVzWG4J0RuEsCAz\nzBvRipUrzY8de8i3IPT0zFuir77aDBE3Oho+3eSxB0AGwNkAHgbw9wAuizVHAENs6YJlCd6xYxcO\nHrwN3d2d2Latcqg1p/BsTU0C69Y9jx/9yPl4P8+6UjjDHTt2YXj4Vk/7AfCURhC8hG4khCQXuliQ\nmiAJi4z4XSzBT5pf+9pDAIZgDn/fVvg7hB/96Kex5zXo0D6Rjx/XHafFNV5++Up897uPwRwwLMfP\ns/bqwlBtP5VuEH5cogghyYMWZKKcaot/lFqLZRznxPh48SIjJ58MrFghJ20ZBFkswV+a3QC+B1Mc\nm2Qy1wcSobLzSktcPMzMzGDHjl04cOAQVq/uxLZtOV/Pz9ka/D9x6ND9AG50LBeVnvWVV+7D5s1b\ni/LidVETt/2q/Wa/B6eccjwA4D/+46dF/1e7N1aHghCSQrz4YQA4H8DjAH4M4GMOv18Hs/X9LoBD\nAF4H8CaH/dQ7nBDtCOoDLMt32Cmdlhbzo4tfsgp/xuI084XIAuEX91CRV69ROfxEu2BkjMrI8M11\nDu+WE9bCNpXKRemzrhTFwmt0i6A+yMW/7RFAa8FP/8HC31YB7PF9b5zKHcsiIfEAlWHeYLphPAGg\nA6YD4/cBnFRl/4sA/J8Kv6m+F0RTvIZuK52kZ4nZXC54yLdKE/9GRvQJJxc0xJa/NPMCWCMWLmwP\n1UiryKsX/IbBY4zaysjo5JTeY1NUHlsoZ97LRdCFb0rz4rZATulvxecdKISns5fp+VUs6+pynia0\nOpW7lpblrpMXCSFqUC2QzwTwoO37DU5WZNvvdwP4kwq/qb0TRGu8LP7hZO1tajKPy+XkR7jQZUES\n9RZkOWmqTFfmeRlhoDqyOjl28dnZ2S0aGjb4vudxdbiKz1tpNcBz5v6vr18WKN64YawuLMvOskhI\n1IQRyF4m6b0FgH0Gzs8K28owDGNBwR3jHzykS2qIUh/g8XHn/ewRJ7ZvBy65BGhoMI/74heB979/\n/tjxceDSS00/ZZV5ioJt23JYtGgvMpnrATyETOb6gh9uLvCEuGpp+mFmZgb9/RuwfPlJWL78Hfjl\nL3+BpqavhE7XL34mXDFGbXVkTYy0T+p74IGvYfHi+32XC1WTNN3em+LzdsKM7GLn4cJ28/+jR0+Y\ni4xRCadyJ4TA0aPnFm1jWSQkAbgpaABrAHzO9v1KALdX2PeDAL5RJS2lPQUSD26xi4P4EluW3QUL\nio9rbjZdLsK6RegYG9myxnV19YjOzm7R1dXrKbaslzS9rrjndHxLy5ttvpkDAmgVixcvE9ns+sDp\nBsGPVVjnuM86oMoFJUh5U5EXL2lOTU2JxsZWAZwkgAsE8CZbOb9GWD7I8ysD7gnkLkILMiHxgQhc\nLB6yfa/oYgFgH4DLq6QlBgcH5z5jtbKGcMpxE5t+F/+wjs/liifSWcflcuHdIsIuSKJiQRMhyht2\nw1hdJvSibFw3bRooa9yB64RhrI60gc/n8yKbXS/q65cV7kn1yVOmQG4tiBtr+eNWCmQbYTtPOufF\nza/ZLEvNwjCs5bFz4phjWsRll60T3d3niFWrThPAaQUXiwEB5D29d/RBJiRexsbGinSmaoFcj/lJ\nesfAnKR3ssN+LQB+DWBBlbSU3xwSD14n4bnhJrZlnScsqizQ5Q17PP6ZFpX8Q4EzIstDqeioq9si\n6uubRTa7vqLIMPO9pyBuLJHjbgGsNdIaXaFSue3q6hWtrSsKnawBUanjGcaqbQnwtrZVoq3tBJHN\nrhdTU1NzHYBsdr3IZtdHes8Z/YXUKkoFspk+zgdwGMB/ArihsG0jgA22fbIA9rqko/pekBiRMeGt\nmmVWN7cIFWK9vGEfqNqQqyZqC7JT4xxkwh0n6bmT5kgflZ5/Z2d3Ybt7xzOoVTuupa+D5CfMvoQk\nAeUCWdaHAjm9RGHZVeXWEAbZUTDKG/a8AFoLIrW8wVJl7Zn3h+4VxxzzJgH8L2H3QW5pWa7kXI2N\nrYVICPPX2tXV69uKrmNDr5tlzmsnQrd8e6HS8z/11B5bOVbTgap2X+PouEUR/SWJZYTUBhTIJFZ0\ns+xGhYpOQSUfRqcJcSonWtnTbWjYKo455k1i6dK3zw0ZyxTHxbF0twhzQlTeweoXrNHWxcdWN8Hu\nJbyal3xHLY4qna90u92toXw0wlo4x3LbyYV6HvZzt7Wtqnhfw4a0C3Kv/ZwzSP50LNuEWFAgk1ix\nLLt2C6/9e5wWXlWo7BR4FXZpiHPsvBrb/AINpt9oT+IbYFn3VKYY9ZInt32iFkeVzhds1b09wjBW\ni/r6Zb46fU5C3OvE2jDlwIooY40m1dVtES0tbw4Um1mmBZnuTERnKJCJFuhgSY7KDUMHdw9VCyxE\nuXBD5UmA5xQ1tDpZg4Mg457KFqNe0nPLt2pxVCpGs9n1Lr7F7vkIU5ac7pnpFrTVdu7KblFhnmHQ\n0IWqfZDjWuiFEC9QIBNtiDvKhA4iPSoqiZNsdn0oK6Ns0VPN6ulsQc4JYE0iLcWVkHFPN20aKBFi\nQmQyW0OJUTex6JZvleLISazV1y9zPN/Che2RiDTn8nqSw7n3iLa2E3wtfe1GJdeNtrZVrsf6Oaff\n/NGCTHSGAploRZzLN09PCzE0VCzSh4bS6eahKubq/AIKuUIaWwMLVTeLVPnvW0VjY6vo6upJpKW4\nEjKsv5UmK3Z19UrJXyW/3mr5VimOnNKutOhGUD91vzh3CNYU3hW1525rO0GURrQBBkRb2wlSz+MX\nq4yYk2vXCOAk0djYKqampiI5NycHkmpQIBNt0MWCnM2apTubTa8FWYhya0+lIWivjXV5Y7cqVGPn\nRUAl3X3CK2Gvs7OzW5iTGO0CKSdWreoKJRK8dGIq5VulD7KzGN0j6uubA/sgh8WpPDc0bBCNja3K\nz63z4jelneqGhuCdaq9wciDxAgUy0QJd3Bt27hTCMITo7TX/7twZ7fnjJOyQt2yLoE7+iXFYm2Se\n0wxRdmyJQFoi6usXhxIJYZ95qYC2okeEvWY3FyKnqC6qO1rVJglGce6WluWFSYBnCMNYLTXcYhji\ncLOgawfxAgUy0QIdJq7VmgW5lLCNhmxBq0sjFsbaFFTkyrZwmT7IG4R9dUDDeJejy4F9YqNbvv08\nc7c0i0VcdygRp6OFMJ8vXyUvyvzoOtoSR0e40jnb2lbR5YLMQYFMEoNqEe3HB1kHQS+bsKJCxQS9\nOFYOKxVxQa8rTP6juJeVJq1ZSyp7ybfXfHq5F7LdAHQShH6jQZSWQRUjGH7TDJuHSsfrYkEGril0\nzvToUJH4oUAmicGvG4ZfEesnfV1cQmQjO4xV2EYmSpFTKf/zK6j5s3CFafhVWNW8+pz7DXvm5Zl7\nuRe6TiSTQZiOhIzJs6X4fVfDvtvVjo+rI2w/Z11drtA5y9PlgsxBgUwShZ+JfKoFddyTCnVEhqCN\na3Z5JRHjVzCaw+gniIaG5YFFbhRWNVkdAi/P3IvgDxOKTHe8dnj8RN8IUxb8lq+w5dHt+Dis/fZz\nmp2zPVI7pCT5UCCTxOEnFJxqERtnWLo0EqfvaCUR09XV68k31vKhNS1RA8KM5BFM2IQdkveKkzAJ\n41JSKR9e0gy6mEUS8HpPzc7JGmH5iZsWze7AHa1K+B2hCDuiodOEWyd0me9A9IICmSSKIII3iIj1\nYk1OkwVZl5igfkK7yc5rtcgHXpbp3bRpoCCirTTyAlhREMnBhqXdrGqq3Fr8pukl3JtbmmYHw36f\nc56WQ9aFauXS6/Wb4c62iHkf7BUCOC31FuS40XFSJ4kfCmSSGIL4/QYVsW7nSpMPsk6Ng5ulSWVe\nK6XtNT60mfdSa19eAGvEwoXtSjoeqoSH3yFvPx0bN8Gvy8Q6P3gVwNWuzYw0srWk7OfEMce0pNoH\nWReSWvaIOiiQSWJQOenOiWriOk1RLKqJm6gty25Cy/n3raKzs1tKHp0aST/+o8UWZPNTV5dTZinT\nZei6sntKjxYjE0KoHSWR0VGpdA9POeV35/za29pWSQsP51cQhhWQXo/XZTSLEApkklpkiNgk+RgH\nbViq+d7GPbu89JyV8gqsUpZHPxEIin2QHxTANUrdBGRbkIOWIad8RLVKnBdUWzBldFQqdf50uYdR\nkARLM6kdKJAJqUCSfIzDNCwyojfIvpZKlibn+KU5YQ8PFlW0h0ouAiqsfTLypjItp2MbG1vLXAbi\n8jtV7QMrI/3K93CDFvcwCsuu7r7KpLagQCbEgaT5GIdpWGSF+4qC0ryaUQ+OFfb4pSryqLN/oqy8\nhRUnpfno6urVpvyodkWR1VEpvYfO7+Ae0dZ2QuTLnkdh2Y3DZYguHaQSYQRyHQjRhHwemJws3jY5\naW4PQkcHsG8f0Ndnfu/rM793dESXl5mZGWzevBXd3edi8+atmJmZqbjvgQOHMDt7dtG22dmzcfDg\nIdfztLe347HHprBx41F0d9+GjRuP4rHHpvAHf3AGMpmHi/bNZB5Gd3envwuRSGleOzv/DQ0NHwDQ\nriyPMzMz2LFjFw4cOITu7k5s25ZDe3u7+4ER0d7ejuHhW3HgwLewbVsOO3bs8lRmSglThkrzMTx8\nK3p63qNN+Vm9ulNpXiq9Q37LSek9LH8HZwBci2efvRiPPjqA3bvr0NV1pq/nHIQdO3bhyJF1mJ29\nBcD5mJ29Bb/5zVq8732XST236udUyszMDLq6zsTu3XWR3k9SAwRV1kE+oAWZVEEni6+MvPi12KgY\nmvQSuituy4tsy1bpNU1NTUl1YVB5v8LeCxX+zLr4k+qUFz+U5tucBHpt2TPKZtcrLVvVfP9l3seo\nnxNdOkg1QBcLkhZ08hkOmxe/FbeqhqXS8L1OgqOai4EfUarSBzSK+yXDRSLJS4XHnRdVHSB7vp1X\nG9wj6uubIy9bZrSWASU+/1GVGV2iwBA9oUAmicQpQsXoqBCXXWaWTCvqRJyh18JEwKhUcbe1rXIN\njxRFw5IEy4sMK7xprVsTqgHN5/Ois7NbmJMJ1d0vP419JTEnqwzpMLoQJVF1GJ3KqIqlqEuxrs8s\nw/ZFTPKJFpRR1mO19k6kAQpkkkic3BgWLjRLZTZr/rZzZ3xuFiosyIAZZ1eHoeEkWF78Nn7VQ8gF\na0DnhcVJyu+Xn3B0KsWcTqMLURGV0HK6t/X1yyJ5F+c7eqvE/DLY+nWM/RBVWa10nqmpKYpmjaFA\nJonFLkJbWoRobp4XxdmsEIYhxNDQ/P5RLe4h0wfZWnbXbrHRoUFKggXZr0XV2cobLg7t/H0aEKUL\niMQVji4JIc+SRpQdxlIrv9eVHmWdO22dnyhG3nSPE06coUAmicZyY8jl5gWota2/v1j8RjWRT5YQ\nz+fzoq3tBAGcUWSx0cFSGzZmbhRWE78WVdPX+FgBbClc09YiK0+QBnReOOULHZz58HSqLFVueVUt\n5pIwuiAbVZ0CL+9K1KJVhqCsNXcD53dijUOHPN0dyaRBgUwSi5Mbg5trQ1jXh6iXmI7TGufWiAVp\nKKNszINZVPOFzsgq0dnZHTpfqtIOIzBoQZZP0HJd7Tn6iSKTza4X2ez6RCzjnEYrtBvOLnPq3a5I\nOCiQSSJxsga3tJgfNwtxmMlzUYeTi6sxUXXeqMXT1NSU6OzsFgsXtovOzm4xNTVVto9Ki6eqyBBh\n0qQPcnDcBK2fDqPbfar2rgS5x7o8F3ag9FtpkjhDgUwSSaUoFqOjxdtKrbsyQsFFHU4ujlBZqhqx\nqH01o/DJVWFpr4aMZxNVyDMdwrvJQrbAdHuO1d6VIGVAF2GaRBccGZb30nfCirFuimTT7aqxsdWx\nE0/igQKZ1Awyrb9hrNBx4rWiV9WIRdlIRxHVIQ6rXBIFRhqQXXbdnmO18wUpA7qUG12Euldkv+P2\nOviyy64QxxzzJmFGBlkjGho2pGa0JQ2EEchcapokijDLR9sZHwfuvBMYHDT/jo/Lzacq/CyrqmrJ\n123bcli0aC8ymesBPIRM5nosWrQX27blQqXrhNelk8MsE+y0BO+RI+uwY8cumZdSRNTL8RKTsEtx\nl+L2HKu9K0HKgC7lJso6QAYy3/HSOvgf/uEpvPZaFsDjAL6G11/frbz+IBERVFkH+YAW5Joj6glx\nXtBpSWu/+LHcqLSMRjX8HoWlKg6rnIoJYcQd2eXJS2zcSpPviiOvrBHASa7D87r4IFt5SYoLjsx3\nvLwM6WHVJ86ALhZEV+IQo26iXEfR7hW/FX2SGjEnohAEcQ0Xy54QRtxRNeHSyS/VyzmmpqZEY2Or\nsFa3a2jY6mmiXpLf6TiQ+Y6X18EDhU8y3E1qDQpkojVRT4hLgoU4qEhPmu+fDKKYjKZKNMm09Nbi\ns1eB6vLk5znxmVZG5jsk8x0vf2Z5AbTOLQjFjqteUCAT7Yl6QlzUotwvQUU8rYhqkCmaVD0jXSZo\nker4eU58ps5EYekPM0GvNG8tLcs9xbAm0UOBTLQmLrEqS5T7sfb62TfofQla0XsNZRalf2safWpV\nWQVpbUwGcVuQ0/BO6V7W6eaSHCiQibaMjpYv/LF4sRA33VS8n2wfYJmi3I+1169lOCrLupcVvaK2\nTKfVGq7KKpjW+5U2/DwnFeHH0lBGaFknsqBAJtriJJAXLjRFsiofYRU+yH4Et33f1lYhhobK8zc9\nHa1l3c0iE4fFRncrUVBUXldSLVdJnhgbBD/PSeYzTcs7lZbrIPFDgUy0xkkIqhSHqhrjXK7c2lsp\nXcsy3N/vLNaHh6OdSOhmkQljsQk6pJtWK1FarHhe8fK+JWHibBrQ9Z3yW0fU2jtE1EGBTLTHyZUg\nSSvZjY2ZlvCmJiGam4tFfmkjXyr+d+4s7wz4EfEyfApVWZDDNGRpthIl1dIbBKdRopaW8iXjdZ84\nmwZ0fKfCxvyuhXeIqIMCmWhN1BZk2ditX1bjv2BBsShw2leI+evs7w/WGZBlSVHlgxymQY5iIRNV\nE5XSMBFKFhMT5rvQ3GyW7+Zm87uTddhPp1gnt4ykPG8dLa86inZSO1AgE21xEowtLeUWJ52HW0sb\naquRz+Xc9xXC9EFesiRYZ0Bm4+Jmkan2eyWBEHZIV4WVSLVIkNlpSYLo8sLYmDm6Aph/ncq4306x\nLm4ZOorOauhmedXV7YPUBhTIRFucBOPoaPnwa1Im7ETdyJc3LnkBrBELF7ZHGoqtkkDQ0TqkOk8y\n0k+a6HJjbMwcVQHMv15HVtzeAx1GmnQs40mC94/ECQUyIREQpJEPO0xc3LjkBbBCANGu2FStgfMb\n0ioKi2lQi5XX/MmwiKVJNExMzLtVDA7Ou1vYy32Y9yDuuQq0gIYjbZ1BkizCCOQ6EEI80dEB7NsH\n9PWZ3/v6zO8dHZWPWbkS6Okp3tbTY273wrZtOSxatBeZzPUAtgD4EIDbAJyP2dlbcOTIOuzYscvv\npfjiwIFDmJ09u2jb7OzZOHjwENrb2/HYY1PYuPEourtvw8aNR/HYY1Nob28v2n9mZgZdXWdi9+46\nPProAHbvrkNX15mYmZkJnb+ZmRls3rwVXV1/gFNPXY2nnvoJDGM7gPm0M5mH0d3dWTUNr/lbvboT\nmczDRdvc0i+l2j1NGs88AxgG8I//CGzfbv41DHO7RdD3YHwcuPNOYHDQ/Ds+LjnzHpDxvGsZr3UE\nIdoRVFkH+YAWZEJ8Y1k2Fy5sj8WSJcPaqcpialmnGho2CODYOes6cK0AWgWwx5PFyk/+ZFjEdLEg\ny5gIp2oynTViMzJi/m8fsYnSJSvs806TrzkhSQN0sSAk/cQlqmQIwmrD1GEExPw9GRBA8b2pq8uJ\ntrYTPKXpdxg97EQoXYaddZkI54QlvO15nJgwBXPUeQyzvLsOz5mQWoUCmZAaIM7GNqwgrCTus9n1\noa5pXtiG8xNV0flwE/66RBvQYSKcG0nIoxO6jBQQUqsoF8gAzgfwOIAfA/hYhX36AHwPwA8BjFXY\nR/GtIGlGp7iocaGLqPJLJXGfza4PJSCqWZD9pCO785E0y2HcE+G8kIQ8lsIJfoTEi1KBDKAOwBMA\nOgBkAHwfwEkl+7QA+HcAbyl8X1YhLfV3g6QWnYeDaxmvLhJO4l5GHGUnH+RMZqtvQSqz85Eky2Gc\n1lmvnV5akAkhQVAtkM8E8KDt+w2lVmQAfw7gJg9pqb0TJPUktaFMK2EtpbJiCm/aNCC6unpEZ2e3\n6Orqjd267kf4xzmJK+5Op5fzx53HMCRtJIGQtKFaIK8B8Dnb9ysB3F6yz04AdwAYA/AogKsqpKX8\nZpD0k8Sh1rQSVuCmVUB4vS9xX78ObktunV4d8hgGlW5RjJBBSHXCCGTDPL4yhmGsAXCeEGJD4fuV\nALqFENfY9hkG8B4AfwhgIYB/A3ChEOKJkrTE4ODg3Pe+vj70WUFlSU2QzwPT08UxUScnzVjCXmID\nj48Da9cCV19txkUdHZ2PSxzF+WWlkRa6u8/Fo48OwJymYPEQurtvw4ED3/KUxszMDHbs2IWDBw+h\nu7sT27blEh8j1YqrfOTIOszOno1M5mEsWrS3LP7r5s1bsXt3HWZnb5nblslcj40bj2J4+NY4si69\nfHtJb/t24MYbzXjH27fHk8+k4bWMEVJLjI+PY9wWMP3GG2+EEMIIlJibgobpYvGQ7buTi8XHAAza\nvv8dgDUOaanrJpBEEGa4VMZQq1Mara1CDA+X71fJQpXkIV/Z0MeyMl4sh7pN4pqeNt8Fe/keGjLf\nEeud8GvNdXtfgrpNJfE9lGnx5btHiDtQ7GJRj/lJesfAnKR3csk+JwH458K+TQAOATjFIa0o7gfR\nnKANoqyh1tLzDw35b2jpC20St4uAH8KKkzDHVzpWN5Fjic6dO82/2awQhmG+I/bf/YrSSu9LaXoj\nI+ZS1aU+yJXe8SS9h7LfFd06V3GTdFccogalAtlMH+cDOAzgPwHcUNi2EcAG2z7XwYxk8QMAmyuk\no/5ukEQQtx9x6fmDNLRxX4MuJCH0nIzV0IIeX+1YHTsY1rvQ22uW72zW+Xe/otTpfSkVNRMTpkAe\nGSk+VzUBnpT3UHZnSLfOVdwkcUSBqEe5QJb1oUAmQqi1+pQ2uNaQsd2KMDQkxJIl5ef309Dar6G1\ndd7CZkHLhV6EFRNhjnc7VscORjZr5rO31/kd9StK/bzz1fYtfb/HxkxBncvpb0GWbfHVsXMVN0ka\nUSDRQIFMEoNbLz/sMFlp+kNDxUPEpd+t81tuFl4qVrdz0HKhH2HFSZjjkzYUbpXnbLbY3SKoz3AQ\ny14lAV667HRLixDNzeb/urx3UbrTyOxcyfCP1iGqRlJGFEg0UCCTxOAmgGUMk5U24FYDX8naOzxs\nWpS9ntPpGipZpYmJn4ZTRSOrswVZJyYmzHJc2tmzRmGCvJ9+O71uAtz6PZczBbL997hHbpLmTuMl\n31GmERZakEkpFMgkVcio5EqtCNWsCrImd3ixXNTiRBI/DaeqRlZXH2TdcCufqsuvVwGuq5VQpTuN\nSuusjE5c3B1B+iATJyiQSeoI0wBWsyCrsip4FfW1WIn7aTj9LLDhVyyEHY6WIW508jPWES8CXGcr\noSp3GtWdLBn5jtuVqBaND8QdCmSSKsI0gLL8g/1Utn5Fr84NvAr8NJxe9k2SRZbIRfcOpiorqmrr\nbBosyDLwU+9TkCcDCmSSKKpVLGEbQC9RLLxUYn7yEaSi1HWIWAWyLchpaIjjRkbjHodA0F2UqOq8\nqbbOlud7q2hsbBWnntrja4Qm6R1XP/W+7p01YkKBTBJFtYpFpwawkqU3bB5rzYIs2wc57qHcNKBq\nVUrVAkGn+qESKtxpougUWvnu6uoVjY2toqFhQyB/+6S7EskKSUj0gAKZJI6kVCxOlt64l8tOIn4a\nTrd9aUGWg4x3MOr3uJbfn6iss9XeLx3CuEWBnxG+WhoNTCIUyCSRyKpYVFmVqjX+cS+XXcuojHSR\nxsa/WpmT8Q5GLRCS0rmWTVTW2UojNF1dPVq7UMiqW2lBThcUyCRxyKxYVFiVvKRJy0F8yBYLafCf\nrIS9LE9Pzy+KY/3t7y+OA+6HuAQC3z11VLIgd3Z2az1yE7XbUK2OZiQNCmSSKFRULE4NdRiLgtux\ntByki7S7bVjltb/fjOqyaVNxCERLLOvug2w/D989NVTqLHZ19Wrv+++lbFSr2xnFIn1QIJNEoapi\nKbUqqWrAoxAGrHyjpRYm/lnvRzZrrijZ319cjqOIYiF7KXmnd++RR8zINXaGh83txBtOIzRJ6US6\njS54rb9ZB6cDCmRS81SyHKiwNkVRcdbC8J1OPr9JafyDUvoeZLPVRYQqZIdxtNK0v3vDw6aVfOdO\n8/vOneb3UtFM/JEENySv9b2X/WqhDq4FKJBJTeNWkSXVXzHNQ8lBG1s3UR1UdCeh8Q9K6fthCcZS\nC3JUhCnXXjun1jX29haLZRIOncO4+RW0XtqFNNfBtQIFMqlpqjWaSa/gkiru3QhisXUTsWFFrs6N\nfxjs74clIoaGit8PP1YxGSMopeXaa5p+RFBvr3mO3l7v+SJ6ocon2E+7kNY6uFagQCbEgaQPkSVd\n3FcjiM+vm6hOu5uEDGSI27DvlVO59pOml/eCFuR0EFeEIos018G1AgUyIQ4keZJF0sW9G0HEOVJk\nwQAAIABJREFUrJuoroWJdroQVDhUKtejo/ORNKw0LSu3E9Wsejr6IOvkb580nMpamImYTu3C6KgQ\nf/u3xduHh4VYvFiIkZHifKSlDq4VKJAJSRlJFvdeCOIOQQuyXgQZeq5UrkdHiycPZrPBrXq6RbFQ\n6d9eK8K7tKzJ7gRNTAjR0mJ+xsbMz6JFQixcWFwG01QH1woUyITUMEkV0359flX6INeK0JCFm0gN\nUia9uEUkcWTFqePW0LBBdHZ2hypvqieW6vJOVCprst1oxsaEaG4WoqlJiAUL5sUySTYUyITUMEkU\nDUFxE9VBJtqlOYKFCryUN79l0trfzYKcxM5guetPXgDHCiAXqrxt2jQgGho2CGBAAOcIwPwuY8RE\nl3fCrRzJnohpWao5KS89UCATUuNwMklw6JrhD68i1U+ZtC+B7cUHOUmUl68BAWwJXd5OPbWnILSv\nKwjw6wRwrOjq6lGQ53jeiWplTYUFefFiIRobiy3IunfASHUokEliiNIClERrUxjSFI4oyuFdTu5T\nh9cymeZRkFJrLHCSlPLW2dldJrSBnOjs7A6dZ93fCVU+yAsXmm4WO3eafxcuNLenoRzWKmEEch0I\niZDpaeDSS4HxcfP7+Lj5fXo62eeKm/Fx4M47gcFB8691zUlkZmYGXV1nYvfuOjz66AB2765DV9eZ\nmJmZUXK+1as7kck8XLQtk3kY3d2dSs6nG/k8MDlZvG1y0tweBj9lsqMD2LcP6Oszv/f1/f/t3X9w\nHOd5H/DvAwJWCFLAkLZBhQkIV/KYGmeOcKL6wDbGAIlqi+50Wg01zMSKnWPikJxWZAyCCuU2aUhN\n6klMj0VSlNqhaqe1OnEwRcOxJSWUnLC8EB4HpNpasJLIv5IUh7itO46bzDBWxrD59I+95e0ddu/2\nx7u77+59PzMY4IC9u8Xeu+8+++yz7+s8nphItg42GB8fx8rKMo4cuYVq9QlUKiMYHPyDtmXitLeB\ngc0A3tPx2weav0/G9n3ivvuAJ58E5uacx3NzzuP77ov3ehMTwCc+AVy+DHz2s8BHPuIcK0SAixeB\n6Wlz604FEjeyjvMFZpBJzZYD9MoSZzFrV97Kln3L+vKuLfWWecl7rNl+Y6q9OTXIJzr2kxM995Mw\nV2f6fZ8o09W4fgeWWFDRmOqAwhyI475Xlgf5JMF4UQL5MBqNho6N7c788m5ZZ9ELy3QNe5naZBq6\ntbew5UVxgtgoz+m3fcJts959YXS0NQ4yFRMDZCoU0wfjbq+X9L2yuvmNGbfWwVtkqnkjk5kMsi3D\nVdkuzIkkA990RQ16owaxttx8ZyO3DnlkpDUWsjs2cj/1w2XDAJkKI61A0O/gbuq9omSgkwQQ/T4S\nRevg3VBg5+278wcG5mJf3u33S8VhhW17PJFLV9oBrO033+VtYcEJiDunQecJYHExQKbCSCMDFXRw\nN/FeUYPWpAFEP9e+tR+8G80s8jt1bOye2AFtnhmzomSuo7bZfj+RS1MaAazbDicnZ3T79nEFPljo\nDHLaVzH6uQ8uIwbI1LeiHtyjdK5xg924AYSpwKOol8HTCGZ7BRxpBbF5Zq7dz9/bDtzHi4vOl5ff\n73q1lzyCiCjtmvuAw22Hzs18l9WZnGRYgV9otssThbuikuZVDJ78lQ8DZOpbUQ+EUTrXJAfZqAGE\nyU6/qJfB0wgquwUcJt4vKMDOM3Ptfv7uxBtnz7YeuzWVSdpGXkFElHbNfcDh1w6BEwpUFditlUq1\nUMGxK402WNQ2Q90xQCaKIO0DfJzX75b1i5P5KmomxPSd890CjqRBbLfXzrvW0/38azVnAgV36uaF\nhWQz1uUdRERp19wHgq+gOFNTB7fHIpQHmb6KUdSrDtQdA2SiiKJ2rmE7z6QBhMkApMy1dFEO4EEB\nR9IgtluAbcNoAe7nPzPTagdu+6rVnN+5gXPY9pVFENHrPfzaddBz5ubKuw+E4Z9BflSB+cD2WIQb\nW4t68kPZY4BMFEGczjVs4JrHjYFpvYaNGo2G1mqHdNOmNzWHg3s20UQLG4PYE1qpVEMF3t0C7LyD\njKAM8tWrrWl5Z2bap+sNknVmrdu+FtSu/Z4zMrJxRIKyiDpWcnsN8pt1cPBwYHu04eSum87P2h15\nwttGo7RPZo7LjQEyUUhJMrQmgs6wnXGS7G/el8HT4h7sBwaONw/2j6ozHFwj1gF8YxB7QkW26ODg\n4VBBba9AIq+JFsLUIEfJIMe5EXZxcWPAsrgYPujw29d6rUfnBA9Ja629/49NAZTfydfo6A6t1Q75\nBszeUSwqlapOTk53bY95lwf12t6df3fHL3Yn9Mjzqh3ZhwEy9a2oB6+kB7ukZQthOuOkgbhtB3RV\nMzWN3S4Xxz2Ae4PYSqXaDI7DZc7yzhIH6TWKhduuotQgR2mTbsDiBqjebG6UoKNzXwvTrt3nzM2Z\n2wdsC6A27gcNBbbdPnFM48a+LDPIYbZ3Z1twJ/WYm4vXZ5b1ihsxQKY+luXBy1Qn2u11bDsYm2Aq\nkOx2w5GJA3iczFnRpuNN0r6inBy6QfHwsOrmze3Z3DDi7GvdnpP0pNGmAGpjO51X4FDz+7sVmNfB\nwcOJh4bL88Sv1/b2a8fDw8mSF2W+Z6OfMUCmvpbFwct04BrUGduY/U3KVEbKP4M8ryJTRg7geWfO\nstDZvlZXVS9caG9ffu0tzj7mtvGoQUecfS3oOW6ph/fv1645l+Oj7r+2BFAb2+m0Am9Wd+ZJ5/ub\ndXJyOvZ7+J34ZT2yRa/t3VlSMzIS/xhg0wkQmcUAmfpe2gevMIFr2OC23zpjUzWNnZmtgYE53bRp\nRGu1Q0YO1jZkzrIWJhiNE7AmySDHOUkMes7iYmvd3cvwWWW009LZToFxBY537F9zWqlUU3vPtPeN\nsNvb7fc3b7Zj5CCyDwNk6mu2HLzSCjaKLigzW6sdipyRSrukoWglEyb02n/iTMZjogbZFO//t3lz\nNhnttHnb6Rvf+FbfE9DJyRlj75fl1ZWw29v9/dzcxhMejmJBLgbI1LdsO3hFCTbcn72dcRk7Zv+7\n7u/S0dEduWZrizAZQhDTB3VTV2C801l7bxB0f5dV2+7cPu7/9wM/EP1E2sSoHGk6enS+OYybN3g9\nYTR4zXJkizBtO+1+3+RVDBvaSD9jgEx9y8ZOKWywYVtwn6bOzGytdshYRipOoFv0cgqTbcfkFRhb\n2rR3Pa5eVd2yxWljw8Ot35XlMnwWbdm2+vy4tfRhJa2DX11tDbPYOZIMZYsBMpElogYbtpSHZC2t\nuuSwwYFtB/w4TLSdNAI/W9q0t+b4zjudgMX7/0UNWGz5v/xkUXpk8wmlLe3Yfc7Bg+2T8Nh0QtVv\nGCAT5chbKhHnTnlb7o7PUpojW4R5nbwnQzAlbtvpNlayiUyXLW3ab6rpsP+f39Wpgwft+L+SiFta\nZHt9fhonMHHasfscdxIeG0+o+gkDZCKPtC+/dXID44UF5+coWSqbs1JpipqRCjqoxw10+z2DnGbJ\ngC1tOul6dG4jd4rugweLu6/anglOyuSJmYmxuN0ZK4t8QlV0DJCJPDoPbOfPOwe28+edx2lc7orT\nmdpc15iFsBmpbgf1uIFu0QOFpG3HWyMZZUa9tNfLFFPrUbZL5nmdGGZxr0jetfRlPKEqAwbIRB06\nO8uzZ9PPakXNXth4g6GNuh3UkwS6tl8y7iZp23EP5m6Gy70cnDTgs6VNm1wPd78+eNDM6+Upr9Ki\ntE+cTL9+0lEs3PVxTzqLekJVBgyQiXx0Bqxp1kXaclm5jHod1Isc6EZlMvBzM1wzM+3ZUWop236d\nZ2lRmtvSlhMzW9enn6UeIAPYB+DLAL4K4DGfv88A+GsA/6P59SsBr5P6xiBSzTaDbMtl5bIqQ72w\nKabaWloZ5DIp+n7tV7efd2mRLTdvUv9INUAGMADg6wAmAAwBeAXAvR3LzAB4LsRrpb0tiDKvQWa2\nIF0mDupFnhSkk4lMXFo1yGVS5P262z6T1xWXPLPxRf4sKZm0A+S9AC57Hn+4M4vcDJCfD/Fa6W4J\nIs1+FAtKX5KDet5ZM9NWVzcONxa1PXNSg3JL46pLkpPMvLLxSYfgpOJLO0B+CMAznsfvB/BkxzIz\nAL7VzC7/LoC3B7xW6huDKA/MUNirbCUa7hURtyzCLR+KcrDnDUXlZvpmvKQnmXn1j50zKroTx4yO\nFr+enMJJEiAPwoz/DmCXqn5HRN4L4DMA3ua34OnTp2//PDs7i9nZWUOrQJSf1VVg/35gcRGYnQXq\ndeDAAeDSJWDXrrzXrr9dv/4q1tfn2363vn4/btx4Iqc1im9pCfi1XwOeeML5Xq0C8/PAuXPA9LTz\n94mJ3m1u167WMtPTTrs9cAD49reBp592Hk9Pp///UDqmpip45ZUrWF/fd/t3Q0NXUK1WYr3emTPn\ncPPmw1hf/xgAYH19H27edH5/4cLHez7f295cWbQvb9t+5BHgu98FXn8dOHnS6aepfOr1Our1upkX\n6xVBwymxeNHzeEOJhc9z/gLAdp/fp3qmQJSnst3xXhZlyiB7M3FumcW+fWYyv7yBqjxMlxXZPPNk\nmOy027aHh9k/9xskyCAPhIihXwbwVhGZEJE3APhpAM95FxCRHZ6fqwBEVb+dOHonykij4WTfvJaW\nnN+HNTvrZCkef9z5zgxFetbW1nDs2AlUq+/BsWMnsLa2FrjsyZNz2Lr10xga+iUAL2Jo6Jewdeun\ncfLkXHYrbMiuXU5WrF4HXngBqNWAl14CfvVXnSxZ3Mxvve5kjk+dcr6bSsBQPsbHx7GysowjR26h\nWn0CR47cwsrKMsbHx2O93tRUBUNDV9p+lyQjbZJ79c5ts/W683h1tfX43DlgeBgYHHT6ZTer3Nnn\nE7UJE0XDGebtKwC+BuDDzd8dAXC4+fMjAP4YwBcBfAHAVMDrpH+6QBSDiZtImEHORpzsWJnGSu5s\nq+5QbZ0TWYS1uNhek+nWai4uJl9XKgfbb3QN6nvdfWVhwfnZ269HmfjDxftKigecKIT6mamOLEmA\nW/QxU4ukTCUTcayuOsGr94B/8KDqnXc6gUBUDJD7Q9KhDm0/yfQrEUpybGCfXg4MkKmvmezI4tZh\nMtuQHZvrIbNy7ZoTxI6MtN+h7wa2Udsir36Um+0Z4Di8fa73RHH7dnPtl/tF8SUJkMPUIBNZy60R\ndmvKTp8GHnwQeOqp6LWYSeow3dpQr+lpjmCRBr96SOBFvP7633StRS4qv/p4APjIRwCR1ogpn/kM\n8Pzzzt+61WT6Yf18ubWPQrEP6+sfw82bD+PMmXN5r1psbu3xk0867f+Xf9mpyz91ylx9MfeLPhc3\nso7zBWaQyTBv9th7p3LcqXezupzGjHN8bjZscPBEM5M8p8CbdXDwcOGzYn66tc2gKx5RM1/MlJVb\nWa66dPabV686pUUHDmysPTbRl3K/KD6wxIL6mXcA+OHh1mXnKEwErN1eo/Nv7iVyt2aU9W3RNBoN\nrVSqCuxWYF6BRqlrkf0O1L0O3mHLhVhrWX5lqdv3a6vDw/HK4uK8F/eL4mGATH3t2jUnOHY7ybw6\nsm4dqt/fRkacIJnZiXjKkhULyxvw9jp4R8l82XY1o9fNZElvNutHy8vLescd2xS4V4GHCn21xdu2\n3Tr8NPpQ2/YLiocBMvW1hYWNgWZeHVm3wMTvb5ycIb6yZMXC6Gw77rBVXm6bj5r5sikQ6HUzWRlv\nNktbKzjercBDCnxQ77hjmy4vL+e9arG5/ebmzczwUncMkKlv2XgZrFvQ6/0b69uSSRIsFSkLmXbA\na9M+1H7S02iWz9yrlUr19mcW5qQozOdbpDYQV6PRaAbHx5tXWx5VYKcODh4u7Imk2z7n5tqHJ1Q1\nc2Jn0wkjJccAmfqWbZ1Z2AyyOySXDUFJkcUZm7VoWci06+NV7TlZa5XNNBTY2QzonBsxt23bqXv2\nTPcsqwnz+RatDcR19Oh88yZW7/Z6VIGHClmKlMXJHMcFLxcGyEQWiFKD7JaFdN64169Ziiyzef1U\nmuEKE1jkWe7jfv5jY/fowMDxZuZ442dUqVR7fnZhPt9+aQNBdfrA7kL+r1kkRLxjjJ861bpXhMmL\nYmKATGSBKKNYeP/W77LO5vXbzX2uqPXxWWn//J9VYJsCb/P9jCYnZ3q2lTCfbxnaQJiTyqNH55vD\nIXr/zzm9445tpcuWhxWmL/aOjjE8zPK3IksSIHOiECIPv0kZlpZaE5J0022yEE4kEizrSQz8JhoZ\nGrqCarWSyvvZImjSg6UlZ2KFxUVnoh130h0TEy2E0f75fwDACoDXAbzYttzQ0BVMT9+HlZVlHDly\nC9XqEzhy5BZWVpYxPj5+e7kwn2/R28Da2homJ/fi4sUBvPzyPC5eHMDk5N4NE+WcPDmHO+/8bQwO\nPgpne87hjjs+hT/8w8tt26yfuBOM9JpIx8nptb5TH4obWcf5AjPIZDmbbljqF1ln82ytP037KkNQ\nljjvqxv+n/+zumnTSOwbMOPWIC8vL+vRo/M6OTmjlUpV9+yZtvIGviglImHr9Ity06KJ9trtism1\na+1DcLrlFjwGFBNYYkGUnNvxeu+S3rq1NZmHKssi0pBHPWicm/vSlubJmc0nfkGff612KPZnFPT5\neoPAWu2Q1mqHbi+zvLzcMUPjcbV1hkbTJ5W2njT6MdWWg2rueZNeuTBAJjLAb9pqQPX8eefvNgUV\nZVKkg3Pa0prgI+8scTdZff693scvUHduFJy37gY+0yeVRbtpMWnNfLfn27yvUHQMkIkMcWe4Gx52\nBqHfsiW9mZqoxcaMbl76cYroLD7/XkFg8IgP77buBr5Go6GjoztUZEqBqopM6ejojtjbrYg3LcYd\ndaVM+w31liRA5k16RB6bNgHf+x7wne8AJ08CL7zgPO68sYnMGh8fx4ULH8f165/DhQsf76sbiLw3\nhtbrwNNPAwcPAk8+2bqRyM/0dOuGutOnne9PPbVxubA3mebJxOd//fp17Nkzha1bd2HPnilcv369\n4++vYn39/rbfra/fjxs3XgXgf+MecAVAxdIb+AQi/xDA483vEvuVinbTorufnDrlfO+2n3SamAAu\nXWr15bOzzuOJCfPrSQUXN7KO8wVmkMlyndNWnz3rPJ6bYwaZ0uFmtM6fb7U57+NemS1vJq1fs2PL\ny8sqskVbM8YdV5EtbdMp98oguyUYrRrkOWtrkE2XRBSpzKlf2zjFA5ZYEAULW1PW2fGeP68qwhpk\nW+V9173JWsWrV1W3b1c9eLC9DfZ6Pb9aSltmxUuL3+deqVSbwbG3RGBOK5Vq2/PCjG7hHcVictLO\nUSzSKIkoSpkTa4QpCgbIRF2EzTh0dryrq6oXLrR3vOyI7WBDxst0JitqTWW3989zVrw0BX3umzf/\noG/AuGXL+IbnFyEI7KVoN9WZYmNwbOM6UQsDZKIeyp5VK7vOrGGtdsiKAMFUu4rzOkEH5oWF7Nt6\nVtn8oMBw+/bxnhlkW5jYVjacIObBxvIKG9eJWhggE4WQZVaNWQVz/IKBTZveFOkSc5oBXNJ2FfcK\nh/vcziscWR+sswzWgkoL3v72f9BRgzy3oQbZBr22VZR2WpZseFQ2JjtsXCdyMEAm6iHrDoxZBXP8\nsoYiUzow0J4x7DaTWFoBnIl29YUvOKU8XhcuOL/3CtOm8jgxizOrW9wTlW7vtby8rJVKVbdsGddK\npZo4OE7jpKrb+vdrVjgOG0uIbFwnYoBM1FVewSqzCmYknYo4rXpNU+0qyuvY2KbC3jBmIgC0ZVKR\nuK85NnaPAlUF5hVotG2rfq0rjsrGfcDGdSIHA2QqLRMZsTzLHZhVSC7pVMRpTYJgehSLsAdY29pU\n2MDOVABow6QiUbkBt3PV47I6M/TtVKBx+3WLOFmHKXFHGrLhypyN60QtDJCptIrc+TCrYEbSbF5R\nMnNhAl8b21TYz6dIAaDpdfWfxnpeRaZub6uitNM09Orn3QDaG0h7H3MUCwrCAJlKLW5QkGfHVeTA\n3kZJsoZFqO0M08ZtblOd4wfv2bNx/OAiBYCm1zUo4B4b2912g17UdprlWOBpv1e3fcDmtk92Y4BM\npRfnsnKenSqzCnax+Y5/k6NYBMmiPYYZocH2ExWXqXV1293Y2G4VmfLUHfsH3FHaaZbbM6v36tbP\n5331hH16MTFAplJL0jHm3akS9ZLFgTeLk8UwWVeTJyppZzSTrmtnUAl8SIFtCjxrJMDMMiOfxXuF\n6avzrL9nFruYGCBTaZnolGy7qYn85T11dNpMB8JRXy/tk8Usa4yLkI32CyoHBuZ0bOweI+07y+2d\n9nuF6eejtt80Tjw712FhgVll2yUJkAdAZLGJCeDSJWB21nk8O+s8npgI9/x6HXj6aeDUKed7vZ7O\nelIya2trmJzci4sXB/Dyy/O4eHEAk5N7sba2Fvv1jh07gWr1PTh27ETs1zFpdRXYv7/VBut15/Hq\najavNzsLPPII8Pjjznd3nzJlaqqCoaErbb8bGrqCarVi9o0AnDlzDjdvPoz19Y8B2If19Y/h5s2H\ncebMOePvFdf1669iff3+tt/duvUA3vKWu3HhwscxPj6e6PWz3N5pv1evfn5pCThwAFhcBE6fdr4f\nOOD8PkjQ/nHjxsbnLS0BjUbrcaPhv8zdd7fvQzt3mt2nyTJxI+s4X2AGmTJk+pIYa9DSY/ISrs3Z\nRdNZ3CivZ/q9OzP+y8vLuc+oZ9OIGGmXJZSxBjlI3L7Xr82HOS4ELXP+/MbXYxmf3cASC6KNTAe0\nrEFLj8mAx/bREkyX/IR5PdNtNyhgWl5ezuRmSNs/Y9Vsgsosbz61+UbXbvz2jzBBbecybnDstw+x\njM9eDJCJMsJsQTriBDxBNcs2ZxfzyiCbPlnMO0DNO6MZlumgsux1+qZ12z/CBLXeZYL2oYUFHhNs\nxgCZKEO9OlaWYkQXNeDptnzewVsQ01ncPK9o2HASUtSMZlxFOSmwRbf9I04GuWhjk5ODATKRAWEC\nW3aa6YkS8HQLgm0NJPIexcIkW09CyiztUTHKJmj/WFzs3T8vLqqOjrYvMzrq/L7zPRYXN9YvLy4y\nIWILBshEBvQKbKMEvizFSFevDGaj0dBa7ZCOjd2jY2O7tVY7xADCIJMnISwbCCeozQPvtOYksAjC\nnFiGDZDd5zIhYi8GyESGdAtso2bseONGsKRBUa8Mpq1Z5DCKUqJjosShyJ9T1vzaPPCoAvOpjJCR\nxklLUdq2ar4jxJA5DJCJDAob2Hbr7NlhBjMRFPV6DdtKAKIEBv2UkbLtc7LZxpn55hXYqa3pq83U\ngKd50lK0th0lycGEiJ0YIBMZEiWwDersL1wo1kEga6aCom4ZTBtuIvPqFRh0BtDuJd25uXKfYNn2\nOdnObfNjY7tVZMoTHJs7sUj7pKUoyQNmkMuBATKRAXGyG34dY5EuI+Yhi6Ao6CBfqx3Kpd51dXXj\nJAPnz7fahF/bGx7OLiOVVx1wP2SQ09i2aWZ5s9g/bc+2RjkWFC0r3m8YIBMZEDewtb2zt00WQZFf\nADE6ukNHR+/Kpd7VPYjWas7/W6ttPIh6T7ZGR1VHRrLJSHVuq4GB47pp00gmNzaWvQY5zf8vrWHu\nmEGOdizwLuv+7F2WyZF8MUAmykkROnvbZBUUdQYQtdqhXLOVZ8+qiqjOzDjfz57duIx7srV5c3YZ\nKf+bv+ZVZCqTYLXM4xkXMUPezzXISa/+2f7/9SMGyEQ5YGcYnxsUTU5Oa6VS1cnJmdSDo7QvHXc7\nuEbJIM/NtQ8x5X2dNAQPH/butrGlORRbdEWtsU7rpMWG8rMw+2mSPp1JE7swQCbKgQ2dfZFlfXnd\ndDav8/O/ds0JbBcWnMfeg2ucGuSsTra6Dx92WScnp0tdBpGmImaQy67XvmYiwGXZnT0YIBNlhEGx\nOVkHD6YDcr8D7eio89V5cI06ioX7nCzalbtdBgaON7Odj6o7fNjQ0KNaqVQZ5MVU9hrrsLJo31He\no1cQnCTAZQbZLgyQiTLCsgpz8rj8bPrSsd/B0O/gavuJlTvz4MDANgXGFfhRFZnS0dEdOjk5U8gy\nAVuUucY6rCz6zajvERQEJwlweXywDwNkogwxQ2BGWS4/ew+0RW4bjUZDR0fvup1JHhg4rqOjd+V+\ncyOVQxb7Rtj3CFouaYBr+4lwP0o9QAawD8CXAXwVwGNdlnsngHUA+wP+nvKmIAonaUfGGrPkynD5\n2W9otqJmj7qNHV30z4nskEW/2es9ugXBDHDLJ0mAPIAeRGQAwFMAHgDwIwDeJyL3Biz3GwBe6vWa\nRHlbXQX27wfqdedxve48Xl3t/dx6HXj6aeDUKee7+xoUzfj4OFZWlnHkyC1Uq0/gyJFbWFlZxvj4\neN6rFsrSEnDgALC4CJw+DVy8CIgAmzY5f5+dBS5dAiYm8lzL8K5ffxXr6/e3/W59/X689tr/LPTn\nRHbIot8M8x4TE85+OTvrPPbup7t2AdPT7ctPTzu/pz7UK4IGsBfAZc/jD8MniwzgQwD+OYDfBDPI\nVABxLvmxxoxcZcs2laXkhexjYw0y9QckyCCL8/xgIvIQgAdU9XDz8fsBVFX1Fz3L7ATwW6r6EyLy\nHwA8r6qXfF5Le70fUZZOnwYef9zJOJw+3Xv5RsPJMnuzDEtLrewDUVGtra1hcnIvbt58GOvr92No\n6Aq2bv00s8WUWBb9Jvtm8iMiUFWJ89xBQ+twDsBjnseBK3PaE4XMzs5i1r3OQZSxzstxs7Oty25B\ndu3a2Nl2XpIjKiK35OXMmXO4ceMJVKsVnDzJ4JiSy6LfZN9MAFCv11E3VL8TJoO8F8BpVd3XfPxh\nOCnrj3qW+XP3RwBvAvC3AA6r6nMdr8UMMllhacmpOV5cdILiet2pJ710iZ0qERFRGSTJIIcJkDcB\n+AqA+wH8bwA3ALxPVV8LWJ4lFmQ9Xo4jIiIqt1RLLFT1+yJyFMDnAAwA+KSqviYiR5yNThZyAAAH\nb0lEQVQ/6zOdT4mzIkRZ4uU4IiIiCtIzg2z0zZhBJiIiIqIMJMkg9xwHmYiIiIionzBAJiIiIiLy\nYIBMREREROTBAJmIiIiIyIMBMhERERGRBwNkIiIiIiIPBshERERERB4MkImIiIiIPBggExERERF5\nMEAmIiIiIvJggExERERE5MEAmYiIiIjIgwEyEREREZEHA2QiIiIiIg8GyEREREREHgyQiYiIiIg8\nGCATEREREXkwQCYiIiIi8mCATERERETkwQCZiIiIiMiDATIRERERkQcDZCIiIiIiDwbIREREREQe\nDJCJiIiIiDwYIBMREREReTBAJiIiIiLyYIBMREREROTBAJmIiIiIyIMBMhERERGRBwNkIiIiIiIP\nBshERERERB4MkImIiIiIPBggExERERF5MEAmIiIiIvJggExERERE5MEAmYiIiIjIgwEyEREREZEH\nA2QiIiIiIg8GyEREREREHgyQiYiIiIg8GCATEREREXkwQCYiIiIi8mCATERERETkwQCZiIiIiMiD\nATIRERERkQcDZCIiIiIiDwbIREREREQeoQJkEdknIl8Wka+KyGM+f/+nIrIiIl8UkRsi8uPmV5WS\nqtfrea9CX+P2zw+3fb64/fPDbZ8vbv/i6hkgi8gAgKcAPADgRwC8T0Tu7VjsD1R1UlV/FMAHAXzC\n+JpSYtxR88Xtnx9u+3xx++eH2z5f3P7FFSaDXAXwNVVdVdV1AAsA/pl3AVX9jufhVgC3zK0iERER\nEVF2wgTIPwRgzfP4L5u/ayMiD4rIawCeB/DzZlaPiIiIiChboqrdFxB5CMADqnq4+fj9AKqq+osB\ny78LwClVfbfP37q/GRERERGRIaoqcZ43GGKZbwDY5Xn8w83fBa3I50XkbhHZrqrfNrGSRERERERZ\nCVNi8TKAt4rIhIi8AcBPA3jOu4CI3OP5+ccAvKEzOCYiIiIiKoKeGWRV/b6IHAXwOTgB9SdV9TUR\nOeL8WZ8B8JCI/CyA7wJ4HcBPpbnSRERERERp6VmDTERERETUT1KdSU9EtonI50TkKyLykoiM+izz\nwyLyX0XkT0TkVRHxvfmPwuk1qUtzmSdF5Gsi8oqIvCPrdSyzEJPqPNycVGdFRD4vIpU81rOswrT/\n5nLvFJF1Edmf5fqVWci+Z7Y5odQfi8jVrNexzEL0PSMi8lyz339VRA7msJqlJCKfFJFvisiXuizD\n425Kem3/2MddVU3tC8BHAZxs/vwYgN/wWeYuAO9o/rwVwFcA3JvmepX1C84Jz9cBTAAYAvBK57YE\n8F4Av9v8eQrAct7rXZavkNt/L4DR5s/7uP2z3f6e5a4AeAHA/rzXuwxfIdv+KIA/AfBDzcdvynu9\ny/IVcvv/SwC/7m57AH8FYDDvdS/DF4B3AXgHgC8F/J3H3Xy3f6zjbqoZZDgTinyq+fOnADzYuYCq\n/h9VfaX5800Ar8FnnGUKpeekLs3HzwKAql4HMCoiO7JdzdIKM6nOsqr+TfPhMtjWTQrT/gHgGID/\nAuD/ZrlyJRdm2z8M4HdU9RsAoKrfyngdyyzM9lcAdzZ/vhPAX6nq9zJcx9JS1c8D+H9dFuFxN0W9\ntn/c427aAfKYqn4TcAJhAGPdFhaRt8A5C7ie8nqVVZhJXTqX+YbPMhRPqEl1PH4BwOVU16i/9Nz+\nIrITwIOq+u8AcNhJc8K0/bcB2C4iV0XkZRH5QGZrV35htv9TAN4uIv8LwAqAD2W0bsTjrk1CH3fD\njIPclYj8PgDvmZDAOVP9FZ/FA+8IFJGtcLI6H2pmkolKS0R+AsDPwbk0RNk5B6fcy8UgOTuDAH4M\nwE8C2ALgj0Tkj1T16/muVt94AMAXVfUnm0Oz/r6I7OHxlvpF1ONu4gBZfWbM86zMN0Vkh6p+U0Tu\nQsAlTREZhBMc/ydV/WzSdepjYSZ1+QaA8R7LUDyhJtURkT0AngGwT1W7XZajaMJs/78PYEFEBE4d\n5ntFZF1VnwMlEWbb/yWAb6nq3wH4OxG5BmASTu0sJRNm+/8cgF8HAFX9MxH5CwD3Avhvmaxhf+Nx\nN2dxjrtpl1g8B+Bg8+cagKDg9zcB/Kmqnk95fcqu56Quzcc/CwAishfAX7tlMJRYmEl1dgH4HQAf\nUNU/y2Edy6zn9lfVu5tffw/OSfm/YHBsRJi+57MA3iUim0RkGM7NSq9lvJ5lFWb7rwL4RwDQrH99\nG4A/z3Qty00QfEWKx930BW7/uMfdxBnkHj4K4D+LyM/D2Tl/CgBE5AcB/HtV/Sci8uMAfgbAqyLy\nRThlGP9KVV9Med1KR0NM6qKqvyci/1hEvg7gb+FkFciAMNsfwL8GsB3Av21mMddVtZrfWpdHyO3f\n9pTMV7KkQvY9XxaRlwB8CcD3ATyjqn+a42qXRsi2/28A/EfPUFgnlTPeGiEinwYwC+CNItIAcArA\nG8DjbiZ6bX/EPO5yohAiIiIiIo+0SyyIiIiIiAqFATIRERERkQcDZCIiIiIiDwbIREREREQeDJCJ\niIiIiDwYIBMREREReTBAJiIiIiLy+P/2C9EGDvi8HAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedae0ab650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "raw_data = loadmat('data/svm_2.mat')\n",
    "\n",
    "data = pd.DataFrame(raw_data['X'], columns=['X1', 'X2'])\n",
    "data['y'] = raw_data['y']\n",
    "\n",
    "positive = data[data['y'].isin([1])]\n",
    "negative = data[data['y'].isin([0])]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.scatter(positive['X1'], positive['X2'], s=30, marker='x', label='Positive')\n",
    "ax.scatter(negative['X1'], negative['X2'], s=30, marker='o', label='Negative')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=100, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape=None, degree=3, gamma=10, kernel='rbf',\n",
       "  max_iter=-1, probability=True, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svc = svm.SVC(C=100, gamma=10, probability=True)\n",
    "svc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9698725376593279"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svc.fit(data[['X1', 'X2']], data['y'])\n",
    "svc.score(data[['X1', 'X2']], data['y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fedacb27ad0>"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iN2/f0OxpU6hcuXJUpkwZcnEaQeXKlqHAwMBCxxUfH09Oo0bR9XPe5HPyKN26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tHT04OOjg6SkpI1rsfFJ2iEPsuMzZs2wc7ODm3btMGKlSvRoEED+Pn7Zzuc4IcoFAq8fPVK\n49rLV6+hkCtyLDPHekTHalx7HR0LiUSMAQMGfBQh4XOQxLRJk7Bzxw6cTEtGz+jXOJLyLnpFtEoF\nhdw4z3XPDba2tqhWrVqm4SsjIyNR0bkcBnToiFUjxqBGpUoYPWKExpz6FKN/+gnPX72Cz+lTeBIR\ngflLlnxVkXX8/P0xdsQwtU4WFubo06Mr/Pbvz7asz8+vuEzn17s1Pf5fbeIhFokwethg+Pn7ZVsX\nLYWL1kDW8p/j5MmTcHR0hN9eXxw+4A/HkiVRurQT1qxehdSEOEyeNBHNmjZFWlparvvy8fHBvTt3\n8eBGEI76+yLy6WM4ly2DAf0HYNfu3RCLxZ9sV79+fbx6E4nV6zZAqVQiKSkJYydNhUeDBjA1Nc21\nXl8zjo6OWLlmDY6JBTgs04WPkRIl3Gtj3sKFn6y/9H//Q3EHB0zs8wPaNWmKSuXLq6ODSCQSpP3r\nuH6qAJAZf9546dGzJ0L0iXC+CzmWRBWCRDoYOHhQHo0wfzEyMkL7du0wfPxExMfHQ6VSYfvuPbh9\n7z6aNWv2xfaXL1/G+AnjMWnMSHTr2B7TJvyEgwcOYMP69bnSq3efPti4bScOHP4DKpUK9+7/hdET\np8Db2ztXcrOLl5cXboSEYdW+I0hLT8fz15EYuHhNtoxjANi6dSt2/Locv0rk2CA3xyypAtuTEnA6\nJQkbkYEhY8fm4yjyh/Fjx0IY9hxdk4AmqUDfdH1sW7ce586d+2JbiUSCihUrQqHI2QNPTEwMNm3a\nhNWrV382tnhOEYtFiInVfCiKiYn97PqbGer5NXb8P/Nrlw9u3818fvXp0wcTZ8xCeMS7GOFBV69h\n1doN6Nm1M6JjYiAWZV8XLYVMTreec1KgdbHQks+kp6fTxsaGJw76qV9znT95lDKplMlvX6pdGerX\nq8t169blur/u3bpx7YplGq/VAo4cZI3q1b/Y9t69e6xerRpNTU1pbGzMNq1b8+3bt7nW6VshMTGR\ngYGBmfqC3rt3jzKhiF0h5kBIOQASuuiL2LXju9TIv//+Oy3EEnZ+/3k7iKgQiXn+/PlM+z5w4ACt\nzS2oEIkpNjLisMGDC/wgWW6Ii4tjl86dKZPJaG5uRpcKFbKcHe7HgQNZtrQTq1SqyGkTxrFp44Z0\nsLPLE//3EydOsHz5cjQ0NKSlpSV/+fnnQnkVf+fOHdZzq00DA30ay6QcPWrkZ1OGfw63KlU5UWLM\n/SaW6tJLKKHUwIBLFi36qlwMsoqliSl/1JNyor5cXerqCjl61Kh87ffs2bM0MzNluxZN2bNjO5oo\nFHnqJ7140SLWqlmD4Q/vU5UQzeMH9tPMzCzHkVM055c5XVy+PL9UKhWnTplCY2NjmigUtLSw4K7N\nG/j47g2WL+fMLVu25EgXLbkDuXCx0Ctk+1yLljzl9u3bkEkl8KhfT32tVs0aKFG8GK5cuw63Wq7Q\n1dVFr66dcfTECfTr1y9X/clkMrx5E6lx7fWbSBhnsoP5N2XKlMGly5cREREBQ0PD//zO8b8RiURw\ndXXNtI6fnx+Kpb9LLgK8SzZSIV2AvQf8AQDt2rVD2OPHmD1zFqhUwsDIEL/88gtq1aqVqdwWLVrg\n6YsIPH/+HKamplmKz/u1EBYWhn379sG1Vi1MnjIFMpkMNjY2WX7lfffuXcjlxjhz9LA6tvCgkaPh\nf/hornXz8PDAzZu3kJycDCMjo2zt2OYlzs7OCDh7DsnJydDX14eeXvZ/6lJSUmD4r3sqFAjQsmVL\njBozJq9ULVCkEgkSY9/C5INhpejrQZ7DXeGsoFKp0K9vX6xbMg+tmjQEANx7EAI3r45o2bJlltbK\nLzFy1ChERkbCuaor9PX1YWxsjK1bt6JYsWI5kieVSrFj505ER0cjMTExS/NLIBBgxsyZGDd+PDas\nX48FCxdi+E/jkZGhxJjRo9E9ExcyLV8nWhcLLf8p5HI53kZFaaQKVSqVePnqNUw++BF4FBoKKyur\nXPfX74cfsHTVavx59hxI4vadu5g0YzYG/vhjlmVYW1t/d8ZxVhGJRFDqaS5T7/yF//HTHj12LF69\njcTdkGBEvH6NXr16ZUm2rq4uHBwcvinjeMf27ahSpQr+un0D1y9fRJ06dXDr1q1s+YMaCYXo072b\nRuKNPt275ciI/BQCgQAikajQjOMPEQqFOR5Xp1494S8g0t/75yaoVDiqK0Cnnj3zUsV8gSTOnj2L\nWbNmYd26dYiPf+cbO3TUSPxpJEA0lSCJYFU6Huiq0DMfxxQWFobExAS0bOyhvlbWyRFVXSrg7Nmz\nedKHjo4O5s2fj4iICNy4cQMPHjyAp6dnruUqFArY2tpma36JRCIMGToUYWFhuHr1GsLDwzF+woSv\nymdbSxbJyjYzAE8AfwEIBjDuE5/XAxAD4Nr7MvkzcvJ3L12LFpKeTZrQu38/RoeHMfbFUw4f7E25\n3JhH/fYy7uUz7ti4jmZmZnkWJ3Svry9LlixJiURCKysrrlyxIk/kaiFfvHhBmUjMphByACTsBQlL\nCCUcN3ZstuRERUVxxYoVnDx5MgMCAr7J1+NxcXFUKBS8ffEMGfeGjHvDM0f8aW1tlS33gXHjxnHU\n0EEa0Sa2rf+NTZo0zkftvz1SU1PZvmVLmonErGlqRmMjIUcNHfrVf3dUKhV7d+9BC7GEVXWMWFZs\nTEtTU4aEhFClUnH6lCk0FktopK/P0sWL8/Tp0/mqT2RkJI2NZYx7dJuql4+pevmYyhePWKaUY46i\nTOSUx48fc97cuZw1c+Z/Mt68lk+D/Azzhne7zA8BOADQB3ADQGl+bCD7Z0FWft8LLVoYFRXFbl27\nUigU0sjIiB07dODGDRtYsaILhUIh67i58ezZs3nap0qlYnR09Dflx/qtcOrUKdpbW9NYKKLI0JA/\n9OnD1NTULLe/d+8ezeQKlhPJWF1gSAuxhL279/jqDZ1/c/LkSbrVciXj3jDk+iXOnDSeU34aTQd7\nO966dSvLch49ekQzMzNuWLWckU8e8fBeH5qbm7FLly6cM3t2luMDfy/cu3ePfn5+uU4+UVAEBATQ\nQizlIIGUw3VkHK4jo5uukC2aeKrrpKenMyYmJstzIDU1lTt37uTYUaO4YcOGLGW9/JBuXbuwc5tW\nfHH7EmMf3uK4od6sXKlSgczB8+fPs23btjSWyTh4YH+OHDKI5ubmXLd2bb73raXwyY2BLOAXwrsI\nBIKaAKaRbPr+7/HvO1zwQZ16AMaQbPkFWfxSf1q05BV/R6kwMDDI976USiX8/f1x9swZ2Nvbo0fP\nnlq3iTxEpVLh+fPnUCgUkEql2WrbyN0d6WcvoyL0AQDpJH4XEXuPHkHt2rXzQ9184c6dO2jerBl+\nnjsDA4ePQfdO7WFkZITV6zdh7E8/YdKkSVmWFRQUhIkTJiDoyhXIjY2RkpKCfj27Iy4+Hjt/34ut\nW7fmKuSblsJjypQpODZnEVwF/7ghJVGFnUYqxCclZlteUlISGtSujbSwJ6iarsQ9Az1EGstwLigI\nZmZmWZKRmJiI0aNHY9u2bUhPT0fLFs3x6/IVeeLmlhmTJk7Etm3bEBcfh6N+e1G9ahUAQHDIQ9Rw\nb4iwsLA88YHW8vUiEAhAMkf+LVlxzrIB8OyDv58DqP6Jeq4CgeAGgHAAY0ney4lCWrTkFQVhGAPv\njOO2bdogIjwcHdp44dqVy1i0eDECAgLg6OhYIDr819HR0YG9vX2O2p67cAG9aYj3oZKhLxDAPiUd\np06d+qYM5HLlyqF48eLoN2QEju7dgxrV3v3Ye/frA+cabrCzs0O3bpq+xZ+jWrVqOH7iBCIiIuDs\n7Iy7QYGwfm+stG3VEv0GD8LDh4++Cj9iLdnD2toaSSJD4IMwvjFQwSKHD+zr1q2DfugTLDAQQmDw\nbhItiYrBovnzsWDx4izJEIvFWL16NVauXAmSWfqO5pbg4GCsXbcOvts3Y8DQEWrjGABKOZZEeeey\nuHLlCjw8PDKRouV7Jq+iWFwFYE8ySSAQNAWwH0CpT1WcPn26+t/u7u5wd3fPIxW0aCkcDhw4gIjw\ncASeOgp9/Xe7lPMX/4LJkyZht49PIWunxcLUDNEvY1EE//woJwoNYWNjU4ha5Yx58+ejQ/v2auMY\nABzs7VCpQnnMnD4dhw8dws5du7J8IOjChQuoW7uW2jgGAPe6bkhJScHz589z/FCipfDo3Lkzpk6c\nhOvJyShDfcRAiXMiHUydOCFH8k4dOoz6hMZ3ykNHD9uOHAGyaCD/TX49cIWGhmLD+vWIjIxE4yZN\n4OXlhbNnz8KzkQdKlSyJV69fIzExUR0XOSMjA4/DwmBtbZ0v+mgpPAICAhAQEJAnsrLybQ0H8OEq\nafv+mhqSCSST3v/7DwD6AoHA5FPCpk+fri5a41jL18Tr16/x85IlGD9uHE6cOPHF7FJ/c+7sWbTz\naqk2jgGgS8d2OHf+fH6p+t1z+/ZtDB86FL26d8eBAwcy/b8aN2kizogEiGAGEqnCFUE6oo300bFj\nxwLUOG9wdHREfEICYmL+SYqQkZGBJ8+ewWfLety6dROnT5/OsjxbW1v8FRyikVnyzZtIJCUlw8Tk\nk0u4lq8chUKBsxcCYVjXFZv1U3HRSoHJC+ZnK7LOh9gXL4an/0rG81SZATsHh7xQN9ecO3cO1atX\nR1JcDEqXKIpZM2egV8+esLGxwf2/gmFhYY6WTT3RrW9//PUgGI8eh6LPwEGoUL4CypQpU9jqa8lj\n3N3dNezM3JAVAzkIQEmBQOAgEAgMAHQG4P9hBYFAYPnBv6sDEJCMypVmWrQUIDdu3ED58uVx5+YN\niA31MHTIYAzo3z9LRrKdnR3u/vWXxrW79/6Cna1tfqn7XbN//37UqVkTF1eux+Ptv2Ngl27wHjDg\ns/W9Bw3CtCWLcdXGFLuFKpg0dse5ixe/qfBuf2NqaopOHTuic9/+uHn7Dh6EhKCP91CUdXJC5You\n8GrmifPZeDCrXr06zM3N0cSrHdp374VOPfuiaduO6Nunzzd5f7S8o3Tp0jh2+hSSU1MRFv4cgwYP\nznGYsSEjR+KAMgOHkhPxVqlEQEoyNinTMTobPu/5ydgxY7B8yUIsmT8Hwwd7I/DkUVy4cAFisRjp\nygyMGDseE8aMhNzYGDXqeaBanfowMbfM0tu9kJAQjB0zBj26d8emTZs0wodq+Q7Iykk+vAvz9gBA\nCIDx768NBDDg/b8HA7gD4DqAQAA1PiMnrw8oatHCuLg4Llm8mB07dOD4ceNydNrcw6MB1yxfqs6G\nl/A6nMWLFctSGKK3b9/SxsaGc6ZPYei9mzzou5v2dnb09fXNyXC0ZIJSqaStpSW9IKQ3pPSGlP0g\nobFQ+N2EbkpLS+P0adMok0kpNzamc5nSXLd8KTNiXrNZk8bZztg1aNAglixRnCt+XsTZUyfTzMyU\nmzZuzB/ltRQaFy5cYJ8ePdiulRd9fHyoVCqz3PbSpUtsWLs2TaVS1qpUicePH89HTbOOSqWiQCBg\nemykRjbTYd4DuXjxYr5+/Zr9f/iBVlZWLF3aib/8/HOWx33+/HmamZlxwphRXLdyGeu61Wazpk2z\ndd+0FD7IzzBveVm0BrKWvCY+Pp4uLhXYvo0Xt29Yy1FDB9PS0jLbxpK+vj4T30RoLLKjhg7m/Pnz\ns9Q+JCSEnTt1oo2NDWvWqKE1jvOJ169fU2xoyB8hURvI3pCynET+XaVy9f39d5qZmXLOtMlcv2IZ\nq1auxIoVyrNkyZKMjo7m6lWr2LZNGw4cMIDXrl37rJxHjx7R1NSU0c/D1DGRr54LoJVV9mIra/m6\n2bJlCxUiMd10hGwAI9qIpezXq3dhq5VrDh8+TBMTBS+fOaVet1UJ0axTuxb37t2bK9l169ThtvVr\n1HLTYyPpUqE8//jjjzzSXktBkBsDWXtEWcs3zbKlS5GakoLk5GTcvH0Ho4YNxsjB3pgze3a25Nja\n2uL+g2CNa/cfBMM2i24SJUuWxM5du/D8+XNcuHgRbdu2zVb/WrKGXC6Hnr4+4j7wiSSIp0kJOHf2\nLGJjYzNp/W0SGxuLeXPnomWL5hg8aBDu37+Pn8b9hL3bNmPimJHo27Mbzhw5gBcvX2L58uXo1rUr\nfHbtRPuWzVDM1gqenk1w5MiRT8q+du0a6tRyhVz+T6iryhVdoKMjQEREREENUUs+kpGRgdHDR6Bx\nElCJ+nAWGKBFIvC7jw8ePHhQ2OrlmAXz52PY0KFo3qQxOvXsg4N/HMHNW7cxeOQYxMTFoUWLFrmS\nH3TlClo1/yfUoZ6eHpo1boSgoKDcqq7lG0FrIGv5ZomIiMCixYvRoF5dDOjbG2lpaahe1wNVKrng\n6rWr2ZI1dswY9BrgjT/PnsPTZ88wddYcPHj4KN8M3ZSUFCz93//Q1NMT3bt1w7lz5/Kln/8a+vr6\nGDdhAk6JBHiCDLyCEseQAgOVCue27IBr1WpISkoqbDXzjKSkJNSrWxe3r19Fv64dYamQws3NDa9e\nvYZbrZrqekKhEE0bN8Lx48fx5EkYjvr9ji4d22HcqOHYsPJXTJgw/pPyHR0dcfX6DQ3fyqfPniEp\nKRkWFhb5Pj4t+c/r16+RlpICC8E/UVwMBALY6Rni2rVrhahZzomNjcX8BQtw+g9/bFn3G+bNmIY5\nCxejbpPmyIAOTp06rXFoOic4OpbEpaB/fkdI4tKVq9rQnd8ReRXmTYuWAmfp//6Hbp06YPnPiwAA\nrZo3g56eHhb+bxmcSjllS9aP3t4wMDDAsJ8m4NWr12jUsCECAgIgFArzXG+S8GrVCjogBvbrjYgX\nL9GpU0csW7oM7dq3z/P+/muMnzABNra2GDloMDISE+EEfTSGEHqpwLEXr7B9+3b079+/sNXME3Zs\n3w6bIpbYvm4VBAIBWrdoBnNTU4yfPht37t1HeeeyAN7F4r4YdAUeDRuhUf160NP7Z2n3bOSBlh26\nvMsM9a+DWi4uLqhcuTLadOmBscOHIi4+DpNnzcXoUaPy5buvpeAxMzMDdHUQQxXkgnd7YkoSL5Rp\ncHLK3jpZ2MTGxsssr4IAACAASURBVGLp//6Hw4cPQSQ0QnjEC9ja2KBT+7bo1L4t6jRqim7dumU5\ngUlmTJ0yFX1+HIz5M6ehRPFi2Lh1O15HRqJNmzZ5MBIt3wQ59c3ISYHWB1lLHuLZpAkP+u7W8Bs+\n6reXpqYmvHTpUoHrEx8fz1kzZ7KOmxvbtG7NEydOaHweEhLCAf3707lsWZYsXpwZcW/VegccOUgn\np1IFrvO3TBFTU/aEhEMFMnWpA0N6DxhQ2KrlGUMGD+Yv82aRsa/V5fHNIJqZmbJkieLctWkdTx3a\nz9YtmrOhhwcPHjzIqpUrURkXSSZEkQlRPH3Yn6VLO322j+TkZM6dM4fVq1Vjvbp1uXnz5m8uDbeW\nzFkwbx4txRI2hZCtIaKjUEJPj4aFrVa2SElJYeXKldilQ3se2e/L/y2cRwtzMx7z30cmxjAm4gkV\nCgXDw8PzrM8jR46wqacnK1euxDGjRzMyMjLPZGspGKD1QdbyPVK2bFkEnNF0TTgR8CcaN26C6tU/\nlewx/1AqlWjSpDFu3biGqePGoEVjD/Tu1Qs+u3cDAB49eoTatWvD2sIUDerVgYd7XY1sUnXdauPh\nw0faMELZoGyZsghHhsa1N2JDVKhUqZA0ynucnZ3x5/kLGtdOnz2PalWrYdHiJdi0cw8mzZqPajVd\n4efvD09PTxgYGqFz7x9w4nQANmzZhh79vTFj+ozP9mFkZIQJEyfi0uXLCPjzT/Ts2TPHIcHygv37\n96NpwwaoVbUK5syereEyk5qaigXz56GWSwU0ql0LPtpEPF9EpVJBYWoKY3NzXBTp4EoRY/SePAH7\nDx0sbNWyxb59+yCTSLB941o0aeSB4YO9sWrpzxg1fiL8Dh5CE6926Na1a54m/2jSpAkO//EHrl69\nhkWLF8M0h9kItXyj5NSyzkmBdgdZSx7y5MkTWllZcdyoETxx0I8Tx45mkSJFGBoaWuC6HDp0iFUr\nV6YqIVq9K3z6jwPqnbshgwdzyvixZGIMTx32p3OZMh/tIJcq5Vjgen/LBAYGUiYSsY6OkF4QsYKh\nhCUcHBgfH1/YquUZ8fHxLFOmNPv17MZj+3y4ePZ0mpmZZhp+8MM3GW3btPnoTca/+XsHuVrVqoW+\ng7xyxQqWtCnCHYM68fj4fvSqXoEN3eup9WnZqBEbWprxdyd7ri9py1IKYy5esKBQdP0WSElJYa0a\nNSkS6NAUOiwPfdoJJezXq1dhq5ZtJk+axOmTxmu8MXz7LJRCIyM29PDg2jVrtCHYtHwEtDvIWr5H\n7O3tceHCBSSnKzF70c+IS0pBYGAgihYtWuC63L9/H26uNTR23urUroUHD4JB8v3nrgAA97p1YGNt\nhaat28Pv4CGsXLMOXfv2x9w5cwtc728ZV1dX/Hn+POzat8SryqXRfMRgXLp69YsJLkJCQtC1Q0c4\n2tujZePGuHz5cgFpnH0kEgnOnj0HK7uimLd0Je6EhOL48RNwff9d+lybyVOm4MzZs/DduxceHh6Z\n9tG5UycEnjuDRbOmYvTggfh58WLMnTMnr4fyRZRKJWbNmI49gzqgY80K0NURID0pCdcuXUDr5s1w\n6NAh3Lx8CZvtzFHXWIKWJjJssTPH/DmzkZaWppbz4sULDOz3A0rZO6BB7do4duzYR33duXMH7Vp5\noYSdPVq3aIGbN28W5FALjNbNWyDsUhAa0hA1YIgXUMIsORW7d+9GeHj4lwV8RbhUrIjjpwL+3mwD\nABw/dRpVq1bF8RMn8EP//nmSylqlUmHVypWoWaMGqlSpjHlz52p8v7R8Pwg+/LLle2cCAQuyPy1a\nCoqTJ09i+LChuHHhrPqA1KEjRzF51lxcv34DY0aPhiotBT8veGcEp6SkoHGrtngbFYVKlSrjR29v\nuLm5FeYQvgueP3+OSuXKo1ZKBpx1dBGqysBRPeBYQACqVq1a2OrlK/7+/vjl558RERGB+vXrY+q0\naXjz5g1atmiBR7euqE/9P332HBVruyM8PLxAD+rFxMTA3tYGUSsn4s+/QtFt2Q7MqVoCLmYy+Ia+\nxvrHb1BNZIRNtpqvuZ3vPsGN4GBYW1sjISEBzqWcUCw6DhVUAryhCsf0gU27dqJly5YA3j0gVa9c\nGRWSMmBLXYQLVLgp1EVg0OX/VOrhe/fuwbVyFXRO1YMu3j24J0AFHySiiEyOzf77Ua9evULWMuuk\np6ejXr26sDA1Rc+unRDy8DGW/LoCe/bsydNxjBk9Gr6+v8PI0AhKpRI6ujooV648fvf1zbM+tBQc\nAoEAJHPkM6bdQdaiJQ9o0KABHByKoolXO+zYvQfzF/+Cvt5DMW/efADAyFGjsGe/PwaPHAPf/X4Y\n8dMEPH0ejpOnTmPb9u3ftXGcnp6OWTNnooS9PYrb2mHqlClITU3Nl75W/PorXNKVaKxnCBsdPbjp\nGaFhhgDzZnzeR/e/wB4fHwwdMgRD+/eB77aNkBoZoG7dOrh9+zaqVHLRCIllb2cLkVCI169fF4hu\nsbGxGDl8GKq6lIcOiHPBT7DQ7xQWVHdETydbuJjKMLNqSTSxVuDs22gkKFXqtjcTk6FvZKQOSbdz\n506YJCShKfRho6OHiroGaJkOTJ8wQd1mycKFKJOiQiUYwFygi4rQh3OqCovnzy+Q8RYUISEhsDIQ\nqo1jAJBABwYQ4HVKEpydnQtRu+yjr6+P48dPoK57fWzcvhuPn4XjxIkTeWocx8bGYs3atbC2ssLq\nZT9j24Y1cHIsiVOnTiE4OPjLArT8p9AayFq05AECgQD79u9Hp85d4HvgMMLCX+DIkSPw9PQEANjY\n2CAoKAgm5pbY5rMXlta2uHTpEooUKVLImhc+/Xr3xub5i1D5WRSqhkdj15L/oVvHTvnSV/Ddu7BR\nar7FchDo4OGD//aP39y5c7Fu+S9o69US5cqWwaI5M1DWqRQiIiJwNvACYmL+SbBy7cZNqMg8Pez0\nOUiiWaOGiLnyJ3y7NsCIuhXR5petuPX0JaqYyzTqVlMIUbxoUbQOe4Vtr6Ox4lUUej6NxIJfflG/\ntQkJDoZFcopGO1sdPYQ+far++6+792D2r++AuRJ4cO9+Po0y70lNTcWkCRNgb2UFeysrTJow4aOH\nysqVKyM8PRkpHyTVeQslUgCMGj06T0KhFTRisRijRo/GgYMH8duaNahQoUKO5Pj5+aF2rVqwtbVF\np44d1cbv/fv3kZGeDr/dO1CvjhuqV62CPds2QyAQICAgIA9HouVbQBsHWYuWf3H8+HHMmjkTfz14\ngEoVK2LW7Nn/Z+++o6K4vjiAfx91C7t0wQIK2LH3LvaONVFj7y1q1ESNJXZ/thhLjF1jScQC9gb2\n3ntXFKUISO+wy97fH5AVrJQFFO/nnDmHnX3z3psBZu/OvLkvQ1kxjIyMMHjIEAweMuSD79va2mJW\nJmf4y+8CAwOx28MD3RMMYZSao7VxPGGblyd8fHx0Pp68bqNG2Hb6HKpr3uYEvisItevX12k7X5oX\nPj6oUrFiunWVK5RHTHQ0evfqjbrNW2PEoP6IiorGslVrsXDhwmxPtJARZ8+eRWRQANaO6wohBMoV\nskLlIgXQe/Mh7H4RjImVU8aTExH2vY7CyEkzoFQqscdtG+QKBXYPG46aNWtq66tVuzbcV6+BSxJB\nL/X3ez9ZhWpVqmvL1G/cCPtv3oFjmmGlL40EmjdyyfH91ZWe3brh1tFjqBGfcjV9x9I/8eTxY+z0\n8NCWsbOzw5ChQ7F17TqUiE2CCsBd/WSM+HE0Zs/9dp932L9/P34cMQJ/LVmECuWcsX3Xbri4uOD2\n7dswNjaGmZkZrKzeDuMxMjJCieJOkMvledhrliey+nRfVhZwFgv2hTt//jzZ2BSgnVs30Wvvx7T+\nr+VkZWVFjx8/zuuu5UtXr16lIkozGiGU6RYHU3M6ffq0ztuLioqisiVKUBWFKf1gJKd6JqZU0MqK\nXr16pfO2MkutVtPcOXPIoVgxsrKyon59+1JQUJBO6m7ZogWtXrqYKDqUKDqUksICqWL58nTo0CHS\naDS0d+9e6te3Lw0fNoyuXLmikzYzYvPmzdStVgVSLxurXVRLx5BCJiUbCzMaWtGJVtZ3pmaOhalO\n1SoUHx//yfpUKhW51K1LpRRK6mggowYyBZmbKOjmzZvaMiEhIVSsSBFylimpiZBQOZmS7AoWIh8f\nHxozahRZmZmTiURKpjI5KaQy6tjOlV6+fJnThyLDXr58SSYSCQ2ACQ2BgoZAQQNgQgqJ9L2/Y41G\nQwcOHKAeXbvRwH796OLFix+s8/Xr19T9u+/JVG5ChQvY0Nw5c77YjBD+/v7Us0cPsrS0pOLFi9Pv\nixZlqq/16talPdv/SZcNo1+vnrRwwQJKSEggc3Mzun3pnPa9196PycTEhAIDA3Nwr1hOQTayWPAV\nZMbS+PnncZg2aSK6dGwPAOjfpxeeej9HwwYNMH/+fPTu0yePe5i/lC1bFlFqFcIJME+dCjeKNHiT\nqELFd6546oJCocDlGzfw999/49KZs2hVsQIGDR4Ma2trnbeVWVMmT8aFs2fgsWktLM3NsfivNWjR\nvDmu37iR7afz5/7vf2jRogXuPXyEEk4O+HenB4oWK4YWLVpACAFXV1e4urrqaE8yrlatWhg3ygfh\ncQkwl0kAAF6PXqKgjQ1OnjuPdWvW4PLTJ+jS0wW9evWCRCL5ZH0GBgY4euIEtm3bhmOHDqOMowO2\nDBsGe3t7EBHWrF6NebNn43VwMOzt7CApUQK9mzTBwIEDMahvP9z1PI4mCQQBPVxFIhJB8DvohbpX\na+Hpi+efbT83+Pv7w8JIAoOEZO06AwiYGxnDz88PdnZ22vVCCLRp0wZt2rT5aH3JycloWKculH6B\n6KTSQ3xsDFbPmYfoyEjMnT8/R/cls1QqFZo2bYr2rVvi9qWzCAwKxogxPyMuLg5Tpk7NUB2+fn5w\nfudhzHJlS8Pn1SsYGxtj6ZKlaNauI4YM6AuZVIa/1q7HrxMnwsbGJgf2iH3RshpZZ2UBX0FmXzA3\nNzeytrKk00cPpru68O/GddTEpSE5OTqSm5tbXncz31m7Zg2ZyWRUQ19KNfSkZC6T09IlS/K6W7kq\nISGBzMzMyO/eDaKw10Rhr0kTGkCVK1b4aB5jjUZDi3//nezt7cjIyIhatWxJDx48+Ggbvr6+NGP6\ndBoyeDC5ubmRSqXKqd3JlJ/HjqHiBQvQnHb1aEzTGmRlpqTDhw/rvJ1169aRjcyEOkJG/WFC9YSE\nLE3NKCQkhPz8/Eghkaa7KjsQJiSDoG6QU3GFGW3btk3nfcqK6OhoUshk1BVyGgwTGgwT6go5KWRy\niomJyXR9hw8fJnuFaboZKfvAhBQyGSUlJeXAHmTdvn37qF6d2unOz8/u3iRLS8sMX0Xu8cMPNOu3\nydrtVZEhVLN6NdqxY4e2zI0bN2jc2LE08scfc+ROFss94CvIjGXfkj/+QOOGDbDVbQca1KsLIOUL\n5L87dqJ929Yo7uiImfMXoWvXnHmA7Fs1cNAgVKteHVs3b4ZGo8GfPXqgevXqn98wH4mOjoZGo4Gt\nTQHtOiEESjo5IiAg4IPbLFu6FFu3bMa+bZvh5FAMG7b8i6ZNm+LBgweQyWQwMDBIl5e7SJEi+G3a\ntJzelUxbsOh3tGrTFnt3e0BpaoaLK/9B8eLFs1SXRqNBQkICZDLZe+/Nnz0bteKSYZv6sVeeDBGe\nlIytW7eiXr16UBoZwSDhbYYMfQiYQCAWGsgTVR/9PeQ2ExMTzJ47FxPGjYMqOeUqsqG+PubP/T1L\n42QDAgJgpkm/TgEBlUqFuLg4mJqa6qLbOuHv74+SxZ3SrStW1B7R0dFITEzMUFrCmbNmoUGDBnj0\n5CkqODvDfe9+WFlbo2PHjtoylStXRuV8NCMnyxrOYsFYqteBgRgzcgTOXbyEpm3a438LF6Nhi9YI\nC4/AgD694OTogMCgwLzuZr5UqVIlLFq8GIuXLPnmguOgoCAMHzYUsbGxUNgVx+CffkZMTCyCgt/A\n69RpNGjQ4IPbLV22FGuX/Y6K5cvBxMQEo4YNRqnijqhRvTqkUikKFSqEPxYvTjexwpdICIHGjRtj\n6fI/MWv27CwHxz+NHg2ZoRHkcjmk+gb45Zdf0r3/JiQUync+8mTxSXgdEABnZ2fEkgYheDtsIRzJ\niIQGSujhlQHQqFGjLPUrJ+x194CTnjF6QI4ekMNJzxj7PHZnqa6GDRviRXIS4ultlPwMajgWKwal\nUvmJLXOfi4sLDh71RGhomHbd9l0eqFypUoZzdjs6OuLu3buoUasOAkPDMeHXX7F33z5tJhTGtLJ6\n6TkrC3iIBctDarWawsPDPzqNbv9+/WjiuDEU+yaARg4bTAVtbWjLutWUGB5MFBtBE8eNof79+uVy\nr9mnJCYmUmRkZJ72ISkpiSIiIrI0PbNGo6Ea1avTLz8Oo8gXDyn40W3q2sGVypctQ4UKFqTZs2Z9\ndFu5XE5hL58SRb0hinpDfo/ukFKhoH/XryZ1eCDdu3yWKpRzptWrVmVn975I0dHR6R7YW7ZsGRlD\nUCfI6EcoqCNkZAxBq9Lse8d2rlRTT0rDoKBhqUMobOQK8vLyIqKUIVYKqZQqGEjJGYZkBEFFYUBW\nMhMaPmRIru/jxzx9+pRMpTIa+M5wEFOpjJ49e5alOif/+itZyORUTU9CFSQKMpWb0Pnz53Xcc92Y\n9OuvZG9nR7/+PJb69uxB1tbWdOnSpbzuFvtCIRtDLHgmPfZN+GvFCsyeMwfR0dGwsbHBwgUL0LFT\np3Rl/P390aBBA5QpWQLlncti/eYtMJHL0bVLZ9y9dx8PnzzFmTNnULhw4TzaC/YftVqN8WPHYe26\ntVCp1ShdvDjWbd6cq7PhaTQazJg+DX8uX47ExCQUd3TA8pWrUD8TKeOuXbuGH7p1xeNLp7XDIeLi\n4mHrXBnu7h5o1qzZR7ft2KEDaletiPE/jQQATJ+7AK/8/LDhr2XaMqfPnceoCVNx+86dLO7ll8Xb\n2xt9e/TA1evXoaenjy5dOmPlmjUo4+gEp+AIlBfG2rK3KBF+ha3x3M8XAPDixQvUrVkTpnFJkMUl\nwk9mgObt2mLzv/9qj723tze2b9+OmJgY6OnpQQiBli1bok6dOumGq+SlS5cu4bsWrdAmKjnd+oNK\nfew8ehi1atXKUr3Xrl3D/v37YWZmhu7du3+xOdqJCJ6enjhz+jQK2Nige/fu2oli8lJcXBwSEhJg\nYWGR111haWRnJj2+p8DyPQ8PDyxZsgSee93hXLYMzpw7j659+qOYg0O6cWaFCxfG3bt3sWvXLvj4\n+GDbNjcAwPnz5/F99x/QpUuXD45tZDmPiBAYGAilUgm5XI5pU6fi4IaNGKg2hAmMcO/JS7Ro0gTP\nfHxgbm6eK33644/FOOqxA1f+mAh7awvsvXgLnTq0x+279zI8yUZYWBgK2dqmC76kUgksLSxgb2//\nyW0XLlqExo0b4fzlq3AqVhR//+OGMSOGpitTpFAhhIWHfaQG3UpMTERISAhsbGxy5Ha1Wq1GkwYN\n4RAUjqEkg0pDOLN7HwapVIiLjYXJO8MnTKCHmOho7WsHBwc8ef4cO3fuhJ+fHxo2bIj69eunO/ZO\nTk6YNGmSzvv+roSEBISGhsLW1hb6+vqZ2rZy5cqIhQZBSIYNUrYNQjJiIbI1brZatWpf/HTrZ86c\nwYgRw+Hr6wchBIYMHgxLS8vPb5iDEhISMHrUKGxzS/m8KFumDNasXZvlSUzYFySrl56zsoCHWLA8\n0LxZM9qx5e90Tz7PmT6VRgwfnuNtv3nzhvz9/XO8nfzs9OnT5GRvTwqJhOTGEho2eDBZKJU0wlBB\nvxmZaZdKJqa0Zs2aj9YTGRlJPj4+OsvvWtLJgS4umUTqQ2u1y6A2jWj+/PkZriMqKorMzc3p9mlP\nohA/ohA/OrhtEzk6OHywnxqNhnx9fSk0NJSIUoYa/P333zRv3jxasWIFlSxRnKL8X2iHXYwZMZQG\nDhigk/39GI1GQwvmzyNLM1OysTCnIgVt6J9//tF5O0ePHqViSjMap2+qXX7UU5LMyJhatmhBdtCn\nEVDQSKGkEVBQYehT586ddd6P7NBoNDRl0iRSSGWklEqpkHUB2rNnT7oyr1+//mz+671795JCKiNn\nqZKcpUpSSGW0d+/enOx6ngsICCBLS0vas/0f0sSEk/+zh9Swfj2aO2dOnvZrxPDh1Kl9Owp59ZzU\nUaG0/q/lVKhQIYqNjc3TfrEU4CwWjH1cZGQkClinn1a1gLU1HjzxzrE2Q0JC0L9fP5w5exb6+voo\nWaIENm3ejJIlS+ZYm/lRUFAQ2rdug6bxGhQXRogD4cg/2xAVHwu5vkm6shJ1MiIjI9+rIykpCSOH\nDMG/29wg0deD0swca7dsRuPGjbPVt6ioaFibKtKts1bKP9iHj1EoFFj5119w6fA9WjVpjMTERJy6\ncBHu7h7v5T6+ffs2+vbpAz9/PyQlqdCieXOsW78efVJzcxMRHty/jzLV66Jdq+a4//AxQiMicPz4\niWzt5+ds374df/+1HBemDYGTjSWuPfdDx9EjUbx48Q/OQBkZGYng4GAUK1YsU7P1RUZGQgYBpJk6\n2RCAEMCy5ctRq0pVbImJhR3pwxfJMFIqsGHDhmzt2399dXBw0MlV8ZUrV2LjkuVwjRcwgT5ex0ej\n9w8/4NK1a5DJZOjWuQvu3rsHgFC1SlVs27Xzg3cjXF1d8eS5NzxSZ87r1KnTFzskQle2bduGDm1b\no33blJzOhQoWxNIF/0OH7j3xay5c9f8QlUqFzVu24Ont67C0TBla0b9PL+zasw/79+/njEdfOc5i\nwfK9tm3bYtnK1UhOTYkUHx+P1ev/RrscnBihb58+cLQvgtfejxDs8xQ9vu+MNm3aaPvAMmbHjh1w\nJD2U0DOEEAJyoQeXBIKxnj6uiLfHMpo0eCQ0aN269Xt1/DZ5Mm6678ZfEgXWGJmgR1QsOru6IjAw\nexlJWrdpg2X7TmqzRIRGxWDrySto165dpuqpVLky7O3ssf+IJ46cOIny5cqjVKlS6cokJCSgdetW\n+GlIfwQ9vouABzehkBhi+LBh2jJCCPy5YgX2HziAshWrYOwv43Hr1u0cD5zWrVyBmZ0aw8km5VZ3\nNcciGNWsFjasW5uuXHJyMn4aPhx2trZoVLUq7G1ssHPnzgy307hxY7xKSkAovf29P4QKTo6OKFGi\nBN5ERuC3RQtQqlM7TPt9IYLCw7KchUGtVmP44CEobGOLOpWroFABG20wmh1Lf1+MEnFJkCNlWEdB\nGKBEErBh/Xq0bt4cdPM+uicaoHuiIeKu3EKHNm0/WpetrS2GDx+O4cOH5/vgGACio6Jg+c74XktL\nC0RHx+RRj1L+ppOSkmBqmv7vLKVf0R/Zin01snrpOSsLeIgFywKVSkV37twhX1/fLG0fGxtLTZo0\npjKlS1Hfnj2oSOHC1KdP7xybSjUwMJDMzc0pISwo3bCOypUq0qlTp3Kkzfxq7ty5VNNIRr8amGqX\nUfoKkhobk6OdHTkpzaiKwowUEinNnT37g3VYm5rRn0pL2m1uo12aKs1o6dKl2epbUFAQVSznTNXK\nlqCezeqTtYUZTfp1YqbqUKvVVKJ4cVqxYDYlB7+kxABvmjh6BDVp3DhduT179lCjBvWIwgO1S4TP\nE5LLszY5hC7VqlqZvCYPJvW/87XLygGdqFf3runKLZw/nyopTWmXhQ15WRWi5aZWZCGTf3Jyk3dt\n2bKFTCRSKq8wo5JKM7I2t6Dbt2/repdo9qxZVExmQn1SM0W0h4yUUhk9efIkS/WFh4dTiyZNyBCC\n5BBkCkHtIaMhUFAtGFOXTp3IWq6gwWkyUwyCCZnJst7m1+Zz5/nr169ToUIF6bX3Y6LYCNLEhNNP\nI4ZRv759c7mn6TVv1owWzpmlPc8/vXODzM3Nyc/PL0/7xVKAh1iw/Or48ePo168fpBIJQsPCUK9u\nXWzesiVTV4ZkMhm8vI7h3LlzePLkCUaP+xmVKlXKsT4nJCTAyMjwvdvHSoUCcXFxOdZufuTq6ooF\ns2ajWrIGSqEHIsIVfQ3at2uHzf/+C09PTwQFBaFx48YoVqzYB+tISEqEzCj9BApSjSbbv4sCBQrg\n+q3bOHbsGPz9/fHbivooUaJEpuq4ePEipBJjDO+fMkzCyMgIMyeOQ6Fy1eHn54ciRYoASLnroVSk\nH84hlUogRMqEDnnJtXMX/OGxDfVLF4OBvj6i4xOx6uQ1TF2wOF25DStXYqgwhKleyoNlpQ2N0Fyj\nwpZNmzB33rwMtdWzZ080a9YMR48ehVwuR+vWrTOc/zYz1q1chSpxGkhSH4KzhT6cVMnYumULZsyc\nmen6BvXrh4Czl9AbcugD8IEanohHR8jgLTfEDy4uuHTsOATe5iIWAIz09L+Jc0ZGzvMODg7o0L4D\nnKvVQrMmjfDkmTcIwNGjnnnXcQArV61C8+bNsXv/ARS0tcXxU6exaOFCznaUD/AQC/bFCg0Nxfff\nf4+NK//E41tX4f/0ASzNlBjz00+Zqufp06e4dOkSqlevjgEDBuRocAwA9vb2KFSoEDZu2apdd+7C\nRdx/+AgNGzbM0bbzG2dnZ0yZOQObDNU4INPDPzKBGAc7LF2xAoaGhmjTpg369+//0eAYADq4umJ3\ncpJ2KERwcjLOa9To0KFDtvunr6+PFi1aoH///pkOjoGUzA9yWfoAT19fH0ZGhkhMTNSua968OU6f\nv4ibd+5q1y1fsx7VqlaFmZlZ1ndAB8aMGQt96yIoPX4Juq7YjhJjF6FKvYbo9E4axcTEJEjeSZUm\n0RAS4uMz1Z6NjQ169+6Nzp0750hwDACJqqT3rh7paTSIz2RfgZQvN/sPHkTVJAEDCAgIOMAQ5tCD\nu2ESeg8aiCFDhiDJQB+voNZu9wJqGCtMUL58+Y/WTUS4d+8erl69CrVa/dFyuhAWFobz589ne2jS\nuz53nici8FP7mQAAIABJREFUzJg+HY6Ojrh06SLUycmIT1Jj4aLfcf36jTxP8ebo6IiHDx9i8tTf\n0LHLd3j06BEGDByYp31iOpLVS89ZWcBDLFgmrF+/nr7v3CndMIU3L71JKpVmaHhEeHg4tWjenAoW\ntKUqlSuRtbX1e0+M55S7d+9S0aJFqVaN6tSkkQtZWlrS0aNHc6Xt/CggIIDc3Nzo1KlTmR4a8+bN\nG6pSrhwVU5pSLQtLUkqktHzJkhzqaeYkJCSQjU0B8nL/lyjElyjEl9YtWUgVK1R4b+IR9127yNzc\nnJo3bkRVK1eikiVKZHpiiMePH9OpU6coKipKl7tBGo2GBvXvR1JDQypnaU6mUimN+XFEun34ZcxY\naqQwpSOWBcnLqhC5WdiQrdyELly4oNO+6MKoH3+kMsZyGpQ65KEn5GQuk9PVq1czVU9CQgJ5enqS\ngb4B9YdcO3xiCBTkJJHT4sWLtWXPnj1L5kolOSrNyCF1+MiVK1c+WverV6+oQtmyZCU3oUIKU7K1\nss6xYzl96lQykUjIycycTFIzyehqiNrnzvPu7u5Utkxp7dCKwOdPqHw5Z3Jzc9NJ+5nx5s0bOnHi\nBL169SrX22ZZg2wMseAAmX2xVq9eTT26fZ/uxBkR8JKMjY1JrVZ/dvt+ffvSoH59KCniDVFsBF06\ndYzMzc0pICAgF3qfMsOap6cn7du3L8/HiX7rNBoNnT9/njw8PD6bQiu3nTp1igoUsKZ6tWtS1UoV\nqVjRonTv3r0Plo2MjKQ9e/bQ8ePHM/Q/8J/o6Ghq26Y1FbS1odrVq5K5uRlt3LhRR3tAtHv3bipp\nbkY3nZ3Ir1IpuluuOFW0MKe///5bWyYmJoaaN2xIBU1MqLalNSklEpozY2aW20xOTqaLFy/SyZMn\nKTExURe7oRUdHU0N6tQhS7kJlVSak1wioXlz52aqDi8vL7IwNSU7pRmZ6OmTAoJ6pI477ggZKaQy\nbbq+/8TFxdHBgwfp8OHDlJCQ8Mn669aoSTX0pdpxyy0gJQtT03QzDOrCwYMHyVauoJH6CvrVwJTG\n6CupmFzxyZSKmfG583znTp1o05qV6d7/Z8Nacm3XTiftZ9TMGTPIzMyM6tetQxYWFjRo4MBM/Q+y\nvJGdAJln0mNfrMDAQJQtWxZe+3ejauVK0Gg0GDdxMgJDwrRJ2T+GiCCXy/Hq0T1YWb1NJN9n8DDU\nrFMPw4cPz+nus0zSaDS4ePEiYmNjUa9evXw7KcuTJ0/w9OlTVKxYUTvGOCEhAadPn4aRkRHq16+f\n4ZRiRISbN28iMDAQtWvX/ugkKaNGjUL4a1+sXzwXhoaGePjkGRp26onzFy7oJPVgV1dX1Lh1Fd0s\nTbXrDkZEY1dhB3ieO5eu7J07d/Dy5UtUr149y9kXnj17hpZNmiIuPByGQg9xegIe+/ZmahbDjLh1\n6xZ8fX1Rs2bNTN3Kj4qKgl2hQmgYq0EhGIBAuIIkPNFLho2JEmHJKmzZ9m+mM578JygoCE5Fi6J7\noiH08XbYipdSH8u3/fPBbC5Z1bVTJ0TuPYwqem9nKXyqUSGgclmcv3Y12/V/7jzfqWNHdGrbCj27\nv02Ztn2XB7bucMf+Awc+WXd4eDguXrwIW1tbVK5cOcuzIR45cgSjRo7EmaMHYWtrg5iYGLTp3BXf\nfd8Vw4YPx4ULF5CQkID69etDIpFkqQ2WM3gmPZYv2draYv26dWjRvjNKFndCwOtA2NnbYffuPRna\nPvUfI906Ivpipoxlbz1//hwtGjdGYngEpEIPwclqbNu5Ay1btsxSfdHR0Th16hSUSiXq1auX6dnK\ncoJKpULfPr1x/PhxVHIuiys3b2PQ4EGYN28+JBIJWrRokan6wsLC0LFDB/j5+sKhqB2u376DBQsW\nYtCgQe+V3bF9O87v26Z9cLRMyeL4oVM77Ny5E5MnT9bJ/hHe+V8DPvi/VqFChWzPMvZ9x46w9Q2G\nM+lDgOALNTq0awf/wECdBiiVKlXK0jMLR44cga2eIQohJSWdgEBVGOGBXgIWb9qA5s2bZ+sL4MfO\nYTlx+emj50sdnUY/d57v1r07Zs+aiZbNmsLKyhJhYeGY/8dSjPv5l0/Wu27tWvwyfjyqVq6EFz4v\nUcSuCPbs2av9Ennz5k28fPkSNWrU+GCuaY1Gg3PnziEyMhLbt7th9PAhsLW1AQCYmJhg0s9jMXX2\n/7B02TKYyGWQy2R46v0cbm5uaNSokW4ODstTHCCzL1rHTp3QomVLXLlyBRYWFihfvnyGAlwhBLp1\n7YpJ02dixR+LYGRkhEtXruLgEU8s+P2PLPcnMTERJ06cQFJSEpo0aQITE5PPb8Q+q+f3XeEY8Aa1\nYQghCK80hK5dusDv9Wso3sne8Dm7d+9G/169UNxYgihNMkipxNFTp+Dg4JBDvc+YZcuWIdjfFy8u\nnYBEYoyw8AjU79gD9es3QNu2H893+zHjx49HGaeiOLFzM/T09PDsuQ/qtOkEFxeX9x4Y1NfXh1qd\nPge3Wp2crS8OKpUKJ0+eRGxsLDp0745pZ8+gsVING0MDhKuT8VdUPH4ePDjL9X+Mr68vvJ95oyvp\nQ6RGaXYwwEMSOH36dKa/aOQEfX3994JVAqAn9NCkSZNs3x0pUKAAKleqjNvX7qBysh4EBHygQpSe\nPpo0aZKtut/Vd9Ag9D3qiRIJGiiEHuKJcFWqj6lDh35+4wz61Hn+u+++w80bN1CiYlU4lymN+w8f\nYUD//vjhhx8+Wt+TJ0/w66RJuHrmBIo7OUKj0WD4T+Mw/pdf8MeSJejcqROePn0K5zKl0b9/f4wb\nOxaTp0zRbv/y5Uu0bt0ahgb6KGBtjSvXrqFahfQPS6qT1fD19cXUib9g+OCUh/JOnDqNrl274uXL\nlzn2ACnLRVkdm5GVBTwGmeWiiIgIat2qFdnYFKAK5cuRjY0N7du3L8v13bx5kwoXLkz16tSmZk0a\nk6WlJXl6euqwx9+mN2/ekMzImKYamtJ0IzPtUtbUnNzd3TNVV1hYGJnKZPSH0pL2WdjSPgtb6ic3\npQY1a+ZQ7zOuTq1a5Om2kTQBT7TLiv9Npz69e2WpPjMzM/K7c4U0wS+1y4gBfWnevHnvlf3555+p\nU5sWFON9hzSvn9LVI7vJ0sKCvL29s9T2o0ePqGjBglTJ0pLqW1mTmUxG3b77jkylUqpcwJpMpVL6\nefSo9x401IWAgAAyMZbQwDQ5g4dAQXYKUzp+/LjO28uKmJgYMlMoqSWkNAQKGggTqmQop9bNm+us\nDV9fX6pcrjxZyORkq1BSoQI2dPHiRZ3Vn9as6dPJRCIlB1NzMpFI6Mdhw3Isj/zHBAUF0enTpykw\nMPCzZefNm0c/Dh2Ubtyy39MHZGZmRuN/+YW6f9eF1FGh2of+itrb0/nz57Xbt2jenOZMn0qamHCi\n2Aha++dSKmBtTS8e3CaKjaCQV8+petUqpFCYaOv5b6lftw4dPnw4Jw8FywRwHmTG3mdqaoqDhw7h\n+fPnCAkJQcWKFWFsbPz5DT+AiNCzZ0/Mm/GbdizcmXPn0aVHD75akE0GBiljNJMBpL2eqQY++ftS\nq9Xw8vJCcHAwGjVqBHt7exw9ehTOxlI4ibc5qNsaSdDr5k1ERETkaUo0I2MjxCckplsXFx8PQyOj\nrNVnZIj4+IR06+ITEj54zGbOnIkB/fvBvlpDFLK1QXBIKFauWgVHR8cstd23a1d0T0xCN3nKHZQH\n+voYdvAgbt6/nzI+1skJ1tbWWar7cwoWLIjKlSvj1tXbqVdPgadQQy1RokGDBjnSZmbJ5XIcOHwI\n33fqjJtx8UhITkb5ChXw99atn9/4E7y9vXH27FkUKVIEjRs3xvU7t/Ho0SPEx8ejYsWKOTaUaMq0\naRgxahQeP34MR0fHPEmtVqBAgQy3a2xs/P7/RnzK/4bHbg+4b92kPVY2NgUwoE9PeLi7o06dOoiN\njcWZs2exZ9tm7VXsgf36YMXa9ahYsx4cHIrh5StfdOvaFU+9nyM5Of2dmP/aYflAViPrrCzgK8js\nK/XkyRMqUriw9orCf0udWjXJy8vrvfKhoaG0efNm2rp1K4WHh+dBj78ubZo3p9oSE5piaErTDE2p\nk76MClhYfPRJfl9fXypuX5RKm5lTPTMLMpVKacH//ke7d++mquZvrx7vs7AlN/MCJDMyoujo6Fze\nq/Q2btxIlcuXI78bZ0kT8ITunz5EdoUL0dmzZ7NU388//0ztW7WgCO97pAl+SSd2u5GlpQX5+/t/\ndBt/f3+6fv36ZzMkfEpwcDApjY3pWhF7umVXVLs0tLamXbt2ZbnezAgICKDa1aqTUiolS7kJFS9W\nLEdm1MsutVpNt27dyvKV+rQmTZhAComUysnNqIjClJxLlqLg4GAd9DL/8fPzI0tLSzp5eD9RbARF\nvn5F7du2ofG//ELlyjnT+eNH053Hx48ZTZMnTSIiovj4eJLL5RTu75OuTIumTWjTpk107do1CgkJ\nIaKUWfTGjxlNieHBlBwdRmtXLCMHBwdSqVR5ufssDXCaN8Z0Q6VS0f79++nPP/+kmzdvatf/d8JN\nDA/WnjA1MeFUzrnse7lHDx8+TObm5tSpvSu1b9uGLC0t6cSJE7m9K1+VkJAQatbQhRQSCVnI5FSi\nWDG6cePGR8t3aNWaOsgUtElpTZuU1vSHiQWZy2R048YNsrGwoDEmprTH3IZ2mttQS4Upfde+fS7u\nzYdpNBqaMmUKmZmZUnFHB7KytKRVq1Zlub74+Hjq27cPmZoqqZi9Pdnb2eXKrd2IiAgyMTamC4Xt\n0gXIVS0t6dChQzneflovXrygR48e5chQji/JxYsXyUImp96puZQHw4QqGMioXq3atH79em3Axt46\nfPgw2dvbU7GiRcnU1JT69e1L8fHx9PuiRVSvTm0KevGUKDaCLp70Imtra3r48KF22969elHfnj9Q\nTLA/aWLCadvf68nW1pZiY2PTtREYGEjNmjYlCwsLMjMzpSJFCtORI0dye1fZJ2QnQOY0b4ylCgkJ\nQdOmTSA1NkaFcs44dNQLrq6u+HPFCggh0LJFC5QtWRxzpk+FgYEBlv21Chu2bsPdu3ehp5cyKWVi\nYiLs7e3h/s8m1KtTGwDgdfwk+g8fiRcvXmQ4fde36vXr14iLi4Ojo+MnH8aUGBnhD4kScvF2MtCt\nmkQ0nzYVTZo0Qa/vvkeAvx/i1GqUKV0a7nv3Znk4ga5FR0fD398fxYoV00nGhdDQUISGhsLJySnX\nsnV87+oKzbnzGCeTw1gI7I6Lxd8G+vD29YVRJoeM3L9/H8eOHUOBAgXQoUMHHq70AZN+/RWe85eg\nGr0dOhQFDdwRBye5En6kwg539yxnfcmvkpOT4e3tDUtLS1haWmrXTZwwAevWr4dSoYCGCEuXLEGn\nzp21212+fBmtW7VCQmIiJMbGUKvVGDp0KOYvWPBeGw8fPkTTpk1RrmwZFLK1xf7DRzB1yhSMzuSM\nryxnZCfNG19BZizV8GHDaMSQQdphFNFBflSmdCntDHjBwcHUrm1bUiqVZGZmRg0a1H/v1um5c+eo\nWpUq6W7NUWwElSld6pNXRL8lGo2GTp06RfPnz6edO3dmaZIHS6WS5svNtVeQNymtqa6pOa1evZqI\niNzc3EgpkVAbcwtqaW5J5nL5V/VAZUJCArm5udGCBQvo3LlzX9wV0oiICOrSti2ZGBuTmVRK1Zyd\n6f79+5mu59fx48lUKqMKxiZUXGFGBa2tMz074Ldg3rx5VME4/UOJHSEjUwgaAgW5QkqWpmY6mzAl\nLCyM1qxZQ7///js9fvxYJ3X+JzY2lrZu3UoLFizI9MyEuhQVFUXe3t4fHA5Rt04dWvPnUgp59Zx8\nHt6h5/dvkbm5Ofn6+r5X1sWlIa34Y5H2XP/q8T2ysLCgFy9e5MJesM8BX0FmLPscHR1wcNd2lCld\nSrtu/u9L8DokDEuWLtWuCwsLg0qlgo2NDVQqFfbv348HDx6gUqVKsLOzg2u7dnjx4Lb2qrJKpYJd\nKWdcvHgpz1ON5bXk5GR0ad8BV06fRkk1IdDIALC2xNlLl2BlZZXheiZNmICDK1dhABlAKfRwWZ2I\nnYYCT318YGRkBDsbGyw1lqOkYcrVzKuJCZhnAPi8fp1nV/Hj4uKwa9cu+Pr6on79+qhfv/4Hr5IH\nBgbCpWEDFLEpgPKlS+DAsVOoW78+Nmz8W/s39aUIDw9HQkICChYsmOltb9++DZc6deAaJyBFyn7d\n1lPD1KUOjhw/puuuftX8/f1RtmQp1I5LRlEYIAaE44iHAwxRESl/4weUenD3PIqaNWtmq60rV66g\nRdOmKJgsYKhOho++BtNmzcLYceOyvR8+Pj5o1MgFZUuVQgknB+zefwjt27fH0mXLvpj89NHR0bCx\nsUFUoG+6c8UP/QaiWcvW6Nevn3ZdfHw8zMzMEB3kl+7OSZ/Bw1C3gQsG50CaQ5Y52bmC/GWdbRnL\nQxYWFngdGJhunf/rAO2tubTlbGxsEB0djXr16mLxooWIjQjD9Gm/YcxPP6FQ4UKYMGUaYmJiEBkZ\niTETJqFihYrffHAMAO7u7rhz5gx+VBmgNYzQL1HAIiAIM3+blql6Zs6Zg8a9e2NKcjxGJEbhgn1h\nHD52DObm5rh8+TKKGku0wTEAVDeWwDBJhUePHul6lzLE19cX5cs5Y8fmjYj09cbAfn3Qt3dvpL1g\n4OPjg4ULF6Jdu3aoU7kCvLatx+JpE3Hbcw9uXLuKw4cP50nfP8Xc3DxLwTEAHD16FMVU0AbHAFBG\no48TZ07rqnv5RuHChbHv0EG8cCiIzYaJ2I5YFII+KiBlyIUGhFiVChYWFtlqh4jQr2dPVI1WoUEc\noXaSHtrF62HalCnw9/fP9n5MGD8e/Xv+gIPubliy4H+4e/ksDh48iAsXLmS7bl0xNjaGgYEBQkPD\n0q33D3j93meBoaEhpFIp3oSEpFsf8Dow278Llvc4QGYs1fBhwzF6/K+4/+AhkpOT4b5nL7bt9EDv\nPn0+WH7pkiVwtLfHWa/D+N/Mabhy+jgkRoZwdW2P56/8YF20OAo6lUZoRNRnp8b+Vhzauw8V4tUw\nSL1aJIRAtWQ9HPnMlLHvMjAwwB9/Lseb8HD4BQbi9qOHqF69OgDAysoKIaokaNIEnwlEiFAlQSqV\nYuvWrZg4fjy2b9+OpKQk3e3cJ0yZNAnd2jTD/vXLMP/XMbh1aAeuX72Mo0ePAkiZ3KRa1ap4fvcG\nqpcpjn2ex7HRzR0AIJVK0KNDW3h6euZY/27evInfpk7FvHnz8OrVqxxrJy0rKyskGBmmWxcDDcwU\nylxpP7fcv38fM6ZPx+zZs+Ht7Z3leho2bIhH3t7wDwxErRo1kWxohCQAiSBcNiRUqFTpvQliMiss\nLAwvXr6EU5oMsCbQg72BBCdPnsxW3QDg6eWFwf3enk+VSiW6de4Iz9T/gy+BkZER+vXti4EjRsE/\nIAAJCQn4fely+PoHvDfG28DAAAMHDMDA4aPg5++PxMRELPnzLzx55p2lyX/Yl4UDZMZS9evfHwMG\nDEQz106QWtrif4uXwsPDA0WLFv1g+WPHjqF/757aW4N6enro16sHLl+6BHcPD4SHhyM8PBzb3Nz4\nakIq28KFEGmQ/kGyCNLAKos5c42NjbVTx/6nfPnysC9REksTYhGl0SBMk4yFiXGoU6cOOrZuhQ0T\nxsFg52Ys+2kkGtaqidjY2CzvT0Z5HfPCgK4dta+lEgm6tW2JY15eSEpKwvBhw3Bg4wr8NWcqVsyZ\ninMeWzFu1nxERccAAF76B+RYXuGF8+ahdcMGCN+wGo+XL0a5kiXQ9bvvcOXKlRxp7z9dunRBiKEe\n7gsVkkGIgAaXZfoY9dPoHG03N61etQp1qtfA3tkLsGvm/1ClfAXs3Lkzy/UJIWBhYYF9hw+hZNvm\n+NcgAf8aJKBk2+bYfWB/tvsrl8shhB7i35kHMFqQTnIfFyhgDZ93voD5vHqFAjY22a5blxYuWoSS\npcugbNVaUNra4djpc/D09PzgA6j/mzcP5StWQrnqdaCwKYL9R7wwbNgwTJk8GZs2bUJCQsIHWmBf\nAw6QGUslhMBPY8bA398f0dHRuHbtOurXr//R8jY2Nnju45Nu3fMXPrBJPdlLJBJOGP+OQUOG4Ka+\nBreSE6Emgo9GhaNGwC9TJuusDSEE9h49AtGkMdqFB6NzZChsXduifOXKKBcXBY/iNvilqA0OlrSF\nZVAAVq9apbO2P9onAM9f+aVb98j7OcLCw/Ho0SOYKRWoWbmC9r1STg4o4+SAi9duYvOuPdh10BN9\n+/bVeb9ev36NuTNn4rCDLaYUssK8QlbYUNQWx3bvhmvjxpg7c5bO2/yPUqnEqXNnQdUrYoOIxVGF\nHvr/PAaT0kz5+zWLiIjAz2PGonW8QI1kA9RS6aNpPDB04KBs37mwsLDATg8PxMbHIzY+Hjs9PHTy\nJVwikaBv3z44LxWIhAaJIFzXV8PIwkwnU1iPGjkKQ0ePw+279xAfH49V6zbi+Omz6N69e7br1pVr\n165h6pQpkEgkOHPmDGJiYnD4yBEUL178g+UNDQ2xYOFChIWFwc/PDyGhITh94jgKmJviny2bUKdO\nbURFReXyXjBd4ACZsXcIITIU2I4cNQrT587D4aNeiIuLg8feffh9+QoMGz48F3r5dXJycsKBo0fx\npLQTJieGw93ECM5Vq+DalSvZuv38LisrK2zzcEdcYiJiExKwbvNmXDhxHF0tZNor/kIIfG8mwanD\nh3TSZmJiIjZt2oShQwZj4cKFCA0N1b4Xn5CAEVPm4NKN24iOicXqf3bg4IkzMDIyQoECBRD0JgSx\ncXHa8mq1Go+f+6BNnyHY4H4ABw4eRJEiRXTSz7QuXLiAWhamKJhmqEM9hQz6AphtKMf8/83Fixcv\nsGnTJgzs2w8LFyxIt1/Z5ezsjHOXLyFJpUJYZCSmzZjxxT2ImFXXr19HAWMJTNN8zFpDH0ZEOhsL\nb2BgoPOHTpcsX47Ow4fgsIke/tGPR8HmLjh17pxOUggOHzECffr2g2vXnlDY2sN9/yF4eXnl+h22\n4OBgzJ83D8OHDcM///yj/cKybOlStG/vComBAKkS0bx5c+zYvj1Dderp6WHVypWo6OyMQ7t3YvzY\n0Ti61wMlHB2w4s8/c3J3WA7hLBaMZcOBAwcwbdpvuH//ASpVrIg5c+fq5ErLt2BQ337w9PBA1UQ1\nYgz0cVVo4L5vHxo3bpwj7XXv2AFV7l3D4MJvH7RZ5BeCkIYtsXL9+izV6efnh3Xr1uLVCx+cu3Ae\nhc1N0cmlFq499saJa3dx9vx5FCtWDDWqVUXdimVw6OQ5vAoIRIMaVWBsbASXVq4YO3YsevXogdjw\nN5g3cQwMDQwwY8lfCIyMxZGjOTfuGAAuXbqE3q1b4YyjrfaLQ4hKjdp3veFuYYtZmiQEmSogQsJQ\nIj4JQcZG8JUY4OK1ayhWrFiO9u1r9/DhQ9SpWg1d4vWgj5RjqwJhh0SNZz5v7zSx3PXkyRO4uLig\nTYtmqFDOGTt374WRRIJ//vkXpUqVwu1LZ1HU3h4AcOfuPTRt1xGvXr3KUM7yZk2bYuyIoWjVopl2\n3b6Dh7Bqw2Yc+gIfsv0WcBYLxnLR3bt3Meann9C/Xz8kJSXh6tVrSEhIwKXLlzk4zqDbt29jz86d\nGJ1sgCaGUrQXRvherYeRgwcjp75E/zTxVywKisTeNxEISVLDLSgcq4Kj8OPYsVmq7/bt26hauRJC\n719HVSsjKPUJxgYCQzq3wcbfxqBvaxfMmjkDADD251+w99gZrJj5K56fOYDm9Wvj6t1H6N27NwBg\n7fr1cHKuAJeu/VGz/Q+QWxfEjp27dLbvH1OzZk1YOzjil4BQvExMwv24BAz29kcriQwSIXA/LgYI\neoOeiQK19CVor9ZD2egETJusuyEx+VWZMmVQtUZ1nDcmREKDMCTjjARo1871mwyOr169ih9HjMCg\ngQNx+PDhHPk/Dw4OxpzZs9G7Vy8sW7oU0dHR75WZ9ttvGD1sCNauWIaRw4bg5OH9SIiLw/Lly1Gp\nQnltcAwAFcqXg5WlBZ48eZKh9osUKYIH79wdePDwMezs7LK3YyxPcIDMWCbs378fTZs2hZmJFNUq\nlsOsmTMwhHNdZtqFCxdQVt8Qxmlyn5bTN8Qzn5eIj4/PkTZr1qyJfzx2Y43EEjXuvsJ2s0LYc/gI\nnJ2ds1Tf5IkTMLVXBywZ1QdDOzTH+ZVzEBoegQPnLgMAOjeph4vnzwMAunXrhtn/m4dfFq5A+VZd\nce7eM5w4eVKb+1kikWDhwkUIeP0awW/eYMWKv6BU5nw2ByEEDhw7BpNW7dD8qR9cH71EYHwS/FUq\njIkJh5FUitJJmnQ5asuSHs6fOZvjfcsP9hw4gMb9e+OYmRHOWsrQeeQwbNyyOa+7les2b9qE9q6u\nKGyhRHkne4wZPQqTJ03SaRuvXr1C1apV8fL5MzSqWwunTx5H3bp13hv/e+HiRXTp2F77Wl9fH51c\n2+Kljw8eP32abnx4ZGQkXgcGZTiV4ajRozH/j2XYum07/AMCsGnrv/h9+Qr8OHKkbnaS5SoeYsFY\nBhERSpUqiVVLfkdjl4YAgNjYWJSqXB2HDh1GhQoVPlMD+8+RI0cwsmt3jFbraYOv1xo1VhsJBIWF\nfhXjUK0tLXBr/XzYWppp183Z5I4YlQbzRg3AloPHsOPCHRw88uWksPqUDRs2YOywYXAhA0iFwCmo\nYVe2DAyePEeb5LfjT28mJyKydjV4cb5ilgFJSUmwt7eD546tqOBcFgAQFh6O4jXq486duzobWz98\n2DCYmcgwd8Zv2nXf9eyDOvUaYEyau0QuDRti5JAB6NzhbZDcZ/AwVKpSDefOnQMlq/DbxPFIUqkw\necZsODoVx+o1azLcj3PnzmHG9Om4d/8+ypcrhxkzZ6J27do62UeWedkZYpE3U0oxlsfUajU2b96M\nA/tGxnGsAAAMq0lEQVT3w9TUFIMGD0adOnU+uU1kZCRevw5Eo4YNtOvkcjmaNnLB1atXOUDOhGbN\nmkFWuCB2vPRDPY0eojQa7DcEfp3y21cRHAOAo0MxXH/yHG1qV9Guu/LgKWpUcMa/R05iwp8b4bYj\n54dJ6IJKpcKEseMwTE+KIvopHwtVSYNZjx5B39AQClUiysAAAZSME0aAR+rQEcY+5+XLl5BJpdrg\nGAAszM1Ru1o13LhxQ2cB8pWrV7Di9wXp1rVv0xoHvU6kWzdh4kQMHDgAyckaVCjnjB0eu3H81Bn8\nsexPDB02DHNmz8b3ffrDwMAAPXv0xPgJEzLVj3r16sHrGM8EmR9k6JNICNFSCPFICPFECPHRvxYh\nRHUhhEoI0Ul3XWRM93r26IGN69fhu/ZtUcm5NL77rgu2f2YyD4VCAblcjoePHmvXaTQaXLtx86Mp\ngNiH6evr4+S5c6jUpxe2mclwwdEOM5YvwxgdTGebWyZNnYbhi9dj54kLuP3MB+NXbsXFh8+w8fAp\nbDl5Fdu274SLi0tedzNDAgICINRqbXAMAFKhh5JSOabPng3TNs3hbi5FcPWKcD9w4KvZL5b3ChYs\niPCISAS8fjtLaVJSEm7du6/T82Zxp+K4cu16unVXr994r41WrVphw4aNWL1xM9p+1w3eL/1w9uxZ\nWFhYQCqVYvacOXjy5CkePHiISZMn59nU9CzvfXaIhRBCD8ATAE0ABAC4CqAbET36QDkvAPEANhCR\nxwfq4iEWLM9du3YN33Xpgkc3r2jTuV24dBk9Bw7Fs2fPPnkFc9nSpVi58i/MmzkNBaytsfSvVQh8\nE4KTJ0+lG6fJvg1HjhzB4oXz4efnjwYuLvht2nQUKlQor7uVafHx8bC1ssLPZAQLvZThFMlEmC2S\ncPziBZQvXz6Pe8i+ZlOnTMHhgwcwa+I4yGUyzF++ElKFKXa5u+usjevXr6Nly5aYMXkiateojgNH\njuKvtRtw7do1FC5cWGftsK9LdoZYZCRArgVgGhG1Sn09EQAR0fx3yo0GkASgOoADHCCzL9W6detw\n/vQpbFy9It16pa0dXr16BTMzs49smcLNzQ2rV61CZFQk2rZpi/ETJsDExCQnu8xYjps9YwbWLfod\nzVWARAicNgDs69bG/iNH8rpr7CtHRFi/bh3+/nsjEhMT0alTZ4wdN07nEyldu3YN8+fNw+PHj1Gt\nWjVMmjyZ7+5943I6QO4MoAURDU593RNADSIalaZMIQD/EFEjIcRGAPs5QGZfqgsXLqBvnz54cP2S\n9vbZzVu30e77H/Dq1auvZgwsY7pERPj333+xaslSxMXF4vtevfDTmDE8GyRj7Kv1JTyktwRA2rHJ\nH+3M9OnTtT+7uLjwWDaW62rXro0SJUrA9bvuGDl0MILfvMH0ufMxMx/N4sVYZgkh0KNHD/To0SOv\nu8IYY1ly6tQpnDp1Sid1ZXSIxXQiapn6+r0hFkKI5//9CMAKQCyAwUS07526+Aoy+yIkJCRg5V9/\nYX9qFoshQ4eiZcuWed0txhhjjOlITg+x0AfwGCkP6b0GcAVAdyJ6+JHyPMSCMcYYY4zlqRwdYkFE\nyUKIHwF4IiUt3HoieiiEGJLyNr2bQZsjYMYYY4wx9tXimfQYY4wxxli+k50ryPxEEmOMMcYYY2lw\ngMwYY4wxxlgaHCAzxhhjjDGWBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlgaHCAzxhhjjDGW\nBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlgaHCAzxhhjjDGWBgfIjDHGGGOMpcEBMmOMMcYY\nY2lwgMwYY4wxxlgaHCAzxhhjjDGWBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlgaHCAzxhhj\njDGWBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlgaHCAzxhhjjDGWBgfIjDHGGGOMpcEBMmOM\nMcYYY2lwgMwYY4wxxlgaHCAzxhhjjDGWBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlgaHCAz\nxhhjjDGWBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlgaHCAzxhhjjDGWBgfIjDHGGGOMpcEB\nMmOMMcYYY2lwgMwYY4wxxlgaHCAzxhhjjDGWBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlga\nHCAzxhhjjDGWBgfIjDHGGGOMpcEBMmOMMcYYY2lwgMwYY4wxxlgaHCAzxhhjjDGWRoYCZCFESyHE\nIyHEEyHEhA+87yqEuC2EuCmEuCKEqKv7rrLsOnXqVF534ZvGxz/v8LHPW3z88w4f+7zFx//r9dkA\nWQihB+BPAC0AOAPoLoQo/U6xY0RUkYgqAxgAYJ3Oe8qyjf9R8xYf/7zDxz5v8fHPO3zs8xYf/69X\nRq4g1wDwlIheEpEKgBuA9mkLEFFcmpcmADS66yJjjDHGGGO5JyMBcmEAvmle+6WuS0cI0UEI8RDA\nfgD9ddM9xhhjjDHGcpcgok8XEKIzgBZENDj1dU8ANYho1EfK1wMwjYiafeC9TzfGGGOMMcaYjhCR\nyMp2Bhko4w/APs3rIqnrPtaRc0IIRyGEBRGF6aKTjDHGGGOM5ZaMDLG4CqC4EKKoEMIIQDcA+9IW\nEEI4pfm5CgCjd4NjxhhjjDHGvgafvYJMRMlCiB8BeCIloF5PRA+FEENS3qY1ADoLIXoDSAIQD+D7\nnOw0Y4wxxhhjOeWzY5AZY4wxxhj7luToTHpCCHMhhKcQ4rEQ4qgQwvQDZYoIIU4IIe4LIe4KIT74\n8B/LmM9N6pJaZpkQ4qkQ4pYQolJu9zE/y8CkOj+kTqpzWwhxTghRPi/6mV9l5O8/tVx1IYRKCNEp\nN/uXn2Xw3OOSOqHUPSHEydzuY36WgXOPUgixL/W8f1cI0TcPupkvCSHWCyGChBB3PlGGP3dzyOeO\nf5Y/d4koxxYA8wGMT/15AoB5HyhjC6BS6s8mAB4DKJ2T/cqvC1K+8DwDUBSAIYBb7x5LAK0AHEz9\nuSaAS3nd7/yyZPD41wJgmvpzSz7+uXv805Q7DuAAgE553e/8sGTwb98UwH0AhVNfW+V1v/PLksHj\n/yuA//137AGEAjDI677nhwVAPQCVANz5yPv8uZu3xz9Ln7s5egUZKROKbEr9eROADu8WIKJAIrqV\n+nMMgIf4QJ5lliGfndQl9fVmACCiywBMhRA2udvNfCsjk+pcIqLI1JeXwH/rupSRv38AGAlgF4Dg\n3OxcPpeRY/8DAHci8gcAIgrJ5T7mZxk5/gRAkfqzAkAoEalzsY/5FhGdAxD+iSL8uZuDPnf8s/q5\nm9MBcgEiCgJSAmEABT5VWAhRDCnfAi7ncL/yq4xM6vJuGf8PlGFZk6FJddIYCOBwjvbo2/LZ4y+E\nKASgAxGtBMBpJ3UnI3/7JQFYCCFOCiGuCiF65Vrv8r+MHP8/AZQVQgQAuA1gdC71jfHn7pckw5+7\nGcmD/ElCCC8Aab8JCaR8U53ygeIffSJQCGGClKs6o1OvJDOWbwkhGgHoh5RbQyz3LEHKcK//cJCc\newwAVAHQGIAcwEUhxEUiepa33fpmtABwk4gap6Zm9RJCVODPW/atyOznbrYDZPrAjHlpOhMkhLAh\noiAhhC0+cktTCGGAlOB4CxHtzW6fvmEZmdTFH4DdZ8qwrMnQpDpCiAoA1gBoSUSfui3HMicjx78a\nADchhEDKOMxWQggV/b+9+3V5Ko7iOP7+IBiMmiyCBrHZRNBgMInZIv6M/gEGQSyCGC0GBTEZBINP\nEK1mQVB4NPgoitFgER4QOYZ7hWsYu2y7d3h9v2CwhcHhsN1z9t3ZTtUGWkaf3H8FvlXVNrCd5CVw\nmGZ2Vsvpk/9LwC2AqtpK8gk4BLwaJcL/m3V3zRapu0OPWGwAF9v7F4BZze8DYLOq7gwcz9TNXerS\nPj4PkOQo8P3PGIyW1mepzj7gCXCuqrbWEOOUzc1/VR1ob/tpPpRfsTleiT7XnqfA8SQ7kuyi+bHS\nu5HjnKo++f8MnARo518PAh9HjXLawuxvpKy7w5uZ/0Xr7tInyHPcBh4nuUzz5jwDkGQvcL+qTic5\nBpwF3iZ5TTOGca2qng8c2+RUj6UuVfUsyakkH4AfNKcKWoE++QeuA7uBu+0p5s+qOrK+qKejZ/7/\nesroQU5Uz2vP+yQvgDfAL+BeVW2uMezJ6Pnavwk87PwV1tVy4+1KJHkEnAD2JPkC3AB2Yt0dxbz8\ns2DddVGIJEmS1DH0iIUkSZL0T7FBliRJkjpskCVJkqQOG2RJkiSpwwZZkiRJ6rBBliRJkjpskCVJ\nkqSO3zM9scClzVd/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedaccd34d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Probability'] = svc.predict_proba(data[['X1', 'X2']])[:,0]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.scatter(data['X1'], data['X2'], s=30, c=data['Probability'], cmap='Reds')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}